Demo ComplexOPs PROCEDUREs and FUNCTIONs

  Notes:  1.  CIS(w) = COS(w) + i*SIN(w), w = -PI..PI
          2.  z = x + i*y


Complex number definition/conversion/output:  CSet/CConvert/CStr

            z rectangular                     z polar
     ---------------------------   -----------------------------
  1    0.00000000 +  0.00000000i    0.00000000*CIS(  0.00000000)
  2    0.50000000 +  0.50000000i    0.70710678*CIS(  0.78539816)
  3   -0.50000000 +  0.50000000i    0.70710678*CIS(  2.35619449)
  4   -0.50000000 -  0.50000000i    0.70710678*CIS( -2.35619449)
  5    0.50000000 -  0.50000000i    0.70710678*CIS( -0.78539816)
  6    1.00000000 +  0.00000000i    1.00000000*CIS(  0.00000000)
  7    1.00000000 +  1.00000000i    1.41421356*CIS(  0.78539816)
  8    0.00000000 +  1.00000000i    1.00000000*CIS(  1.57079633)
  9   -1.00000000 +  1.00000000i    1.41421356*CIS(  2.35619449)
 10   -1.00000000 +  0.00000000i    1.00000000*CIS(  3.14159265)
 11   -1.00000000 -  1.00000000i    1.41421356*CIS( -2.35619449)
 12    0.00000000 -  1.00000000i    1.00000000*CIS( -1.57079633)
 13    1.00000000 -  1.00000000i    1.41421356*CIS( -0.78539816)
 14    5.00000000 +  0.00000000i    5.00000000*CIS(  0.00000000)
 15    5.00000000 +  3.00000000i    5.83095189*CIS(  0.54041950)
 16    0.00000000 +  3.00000000i    3.00000000*CIS(  1.57079633)
 17   -5.00000000 +  3.00000000i    5.83095189*CIS(  2.60117315)
 18   -5.00000000 +  0.00000000i    5.00000000*CIS(  3.14159265)
 19   -5.00000000 -  3.00000000i    5.83095189*CIS( -2.60117315)
 20    0.00000000 -  3.00000000i    3.00000000*CIS( -1.57079633)
 21   -5.00000000 -  3.00000000i    5.83095189*CIS( -2.60117315)


Complex arithmetic:  CAdd, CSub, CMult, CDiv

   Let z1 =     1.000 +   1.000i or    1.414*CIS(   0.785)
       z2 =     1.732 -   1.000i or    2.000*CIS(  -0.524)

  z1 + z2 =     2.732 +   0.000i or    2.732*CIS(   0.000)
  z1 - z2 =    -0.732 +   2.000i or    2.130*CIS(   1.922)
  z1 * z2 =     2.732 +   0.732i or    2.828*CIS(   0.262)
  z1 / z2 =     0.183 +   0.683i or    0.707*CIS(   1.309)


Complex natural logarithm:  CLn = LN(z)

  Notes:  1.  LN(z) is multivalued.
          2.  Any multiple of 2*PI*i could be added to/subtracted from LN(z).
          3.  LN(1)=0; LN(-1)=PI*i; LN(+/-i)=+/-0.5*PI*i.

                              LN(z)
          z                rectangular                EXP( LN(z) ) = z
     ------------  ---------------------------  ---------------------------
  1   0.0 +  0.0i           undefined
  2   0.5 +  0.5i  -0.346573590 + 0.785398163i   0.500000000 + 0.500000000i
  3  -0.5 +  0.5i  -0.346573590 + 2.356194490i  -0.500000000 + 0.500000000i
  4  -0.5 -  0.5i  -0.346573590 - 2.356194490i  -0.500000000 - 0.500000000i
  5   0.5 -  0.5i  -0.346573590 - 0.785398163i   0.500000000 - 0.500000000i
  6   1.0 +  0.0i   0.000000000 + 0.000000000i   1.000000000 + 0.000000000i
  7   1.0 +  1.0i   0.346573590 + 0.785398163i   1.000000000 + 1.000000000i
  8   0.0 +  1.0i   0.000000000 + 1.570796327i   0.000000000 + 1.000000000i
  9  -1.0 +  1.0i   0.346573590 + 2.356194490i  -1.000000000 + 1.000000000i
 10  -1.0 +  0.0i   0.000000000 + 3.141592654i  -1.000000000 + 0.000000000i
 11  -1.0 -  1.0i   0.346573590 - 2.356194490i  -1.000000000 - 1.000000000i
 12   0.0 -  1.0i   0.000000000 - 1.570796327i   0.000000000 - 1.000000000i
 13   1.0 -  1.0i   0.346573590 - 0.785398163i   1.000000000 - 1.000000000i
 14   5.0 +  0.0i   1.609437912 + 0.000000000i   5.000000000 + 0.000000000i
 15   5.0 +  3.0i   1.763180262 + 0.540419500i   5.000000000 + 3.000000000i
 16   0.0 +  3.0i   1.098612289 + 1.570796327i   0.000000000 + 3.000000000i
 17  -5.0 +  3.0i   1.763180262 + 2.601173153i  -5.000000000 + 3.000000000i
 18  -5.0 +  0.0i   1.609437912 + 3.141592654i  -5.000000000 + 0.000000000i
 19  -5.0 -  3.0i   1.763180262 - 2.601173153i  -5.000000000 - 3.000000000i
 20   0.0 -  3.0i   1.098612289 - 1.570796327i   0.000000000 - 3.000000000i
 21  -5.0 -  3.0i   1.763180262 - 2.601173153i  -5.000000000 - 3.000000000i
 22 -20.0 + 20.0i   3.342305864 + 2.356194490i  -20.000000000 +20.000000000i


Complex exponential:  CExp = EXP(z)

                             EXP(z)
          z                rectangular                LN( EXP(z) ) = z
     ------------  ---------------------------  ---------------------------
  1   0.0 +  0.0i   1.000000000 + 0.000000000i   0.000000000 + 0.000000000i
  2   0.5 +  0.5i   1.446889037 + 0.790439083i   0.500000000 + 0.500000000i
  3  -0.5 +  0.5i   0.532280730 + 0.290786288i  -0.500000000 + 0.500000000i
  4  -0.5 -  0.5i   0.532280730 - 0.290786288i  -0.500000000 - 0.500000000i
  5   0.5 -  0.5i   1.446889037 - 0.790439083i   0.500000000 - 0.500000000i
  6   1.0 +  0.0i   2.718281828 + 0.000000000i   1.000000000 + 0.000000000i
  7   1.0 +  1.0i   1.468693940 + 2.287355287i   1.000000000 + 1.000000000i
  8   0.0 +  1.0i   0.540302306 + 0.841470985i   0.000000000 + 1.000000000i
  9  -1.0 +  1.0i   0.198766110 + 0.309559876i  -1.000000000 + 1.000000000i
 10  -1.0 +  0.0i   0.367879441 + 0.000000000i  -1.000000000 + 0.000000000i
 11  -1.0 -  1.0i   0.198766110 - 0.309559876i  -1.000000000 - 1.000000000i
 12   0.0 -  1.0i   0.540302306 - 0.841470985i   0.000000000 - 1.000000000i
 13   1.0 -  1.0i   1.468693940 - 2.287355287i   1.000000000 - 1.000000000i
 14   5.0 +  0.0i   148.4131591 +   0.0000000i     5.0000000 +   0.0000000i
 15   5.0 +  3.0i  -146.9279139 +  20.9440662i     5.0000000 +   3.0000000i
 16   0.0 +  3.0i  -0.989992497 + 0.141120008i   0.000000000 + 3.000000000i
 17  -5.0 +  3.0i  -0.006670517 + 0.000950859i  -5.000000000 + 3.000000000i
 18  -5.0 +  0.0i   0.006737947 + 0.000000000i  -5.000000000 + 0.000000000i
 19  -5.0 -  3.0i  -0.006670517 - 0.000950859i  -5.000000000 - 3.000000000i
 20   0.0 -  3.0i  -0.989992497 - 0.141120008i   0.000000000 - 3.000000000i
 21  -5.0 -  3.0i  -0.006670517 - 0.000950859i  -5.000000000 - 3.000000000i
 22 -20.0 + 20.0i   0.000000001 + 0.000000002i  -20.000000000 + 1.150444078i


Complex power:  CPwr = z1^z2

                            z^(-1+i)                     z^(-1+i)
          z                rectangular                     polar
     ------------  ---------------------------  -----------------------------
  1   0.0 +  0.0i           undefined
  2   0.5 +  0.5i   0.273957254 - 0.583700759i  0.644793884*CIS(-1.131971754)
  3  -0.5 +  0.5i  -0.121339466 - 0.056950118i  0.134039479*CIS(-2.702768080)
  4  -0.5 -  0.5i  -6.339560605 +13.507239848i 14.920977079*CIS( 2.009620900)
  5   0.5 -  0.5i   2.807879297 + 1.317865173i  3.101766394*CIS( 0.438824573)
  6   1.0 +  0.0i   1.000000000 + 0.000000000i  1.000000000*CIS( 0.000000000)
  7   1.0 +  1.0i   0.291850379 - 0.136978627i  0.322396942*CIS(-0.438824573)
  8   0.0 +  1.0i   0.000000000 - 0.207879576i  0.207879576*CIS(-1.570796327)
  9  -1.0 +  1.0i  -0.028475059 - 0.060669733i  0.067019740*CIS(-2.009620900)
 10  -1.0 +  0.0i  -0.043213918 + 0.000000000i  0.043213918*CIS(-3.141592654)
 11  -1.0 -  1.0i  -6.753619924 + 3.169780303i  7.460488539*CIS( 2.702768080)
 12   0.0 -  1.0i   0.000000000 + 4.810477381i  4.810477381*CIS( 1.570796327)
 13   1.0 -  1.0i   0.658932586 + 1.403939649i  1.550883197*CIS( 1.131971754)
 14   5.0 +  0.0i  -0.007726394 + 0.199850701i  0.200000000*CIS( 1.609437912)
 15   5.0 +  3.0i   0.034070593 + 0.093909115i  0.099898585*CIS( 1.222760762)
 16   0.0 +  3.0i   0.061710926 - 0.031516790i  0.069293192*CIS(-0.472184038)
 17  -5.0 +  3.0i   0.008511047 - 0.009456941i  0.012722879*CIS(-0.837992891)
 18  -5.0 +  0.0i   0.000333888 - 0.008636332i  0.008642784*CIS(-1.532154741)
 19  -5.0 -  3.0i  -0.788417122 - 2.173121965i  2.311722438*CIS(-1.918831892)
 20   0.0 -  3.0i  -1.428033572 + 0.729320361i  1.603492460*CIS( 2.669408615)
 21  -5.0 -  3.0i  -0.788417122 - 2.173121965i  2.311722438*CIS(-1.918831892)


Complex cosine:  CCos = COS(z)

                             COS(z)                       COS(z)
          z                rectangular                     polar
     ------------  ---------------------------  -----------------------------
  1   0.0 +  0.0i   1.000000000 + 0.000000000i  1.000000000*CIS( 0.000000000)
  2   0.5 +  0.5i   0.989584883 - 0.249826398i  1.020632877*CIS(-0.247288622)
  3  -0.5 +  0.5i   0.989584883 + 0.249826398i  1.020632877*CIS( 0.247288622)
  4  -0.5 -  0.5i   0.989584883 - 0.249826398i  1.020632877*CIS(-0.247288622)
  5   0.5 -  0.5i   0.989584883 + 0.249826398i  1.020632877*CIS( 0.247288622)
  6   1.0 +  0.0i   0.540302306 + 0.000000000i  0.540302306*CIS( 0.000000000)
  7   1.0 +  1.0i   0.833730025 - 0.988897706i  1.293454455*CIS(-0.870327425)
  8   0.0 +  1.0i   1.543080635 + 0.000000000i  1.543080635*CIS( 0.000000000)
  9  -1.0 +  1.0i   0.833730025 + 0.988897706i  1.293454455*CIS( 0.870327425)
 10  -1.0 +  0.0i   0.540302306 + 0.000000000i  0.540302306*CIS( 0.000000000)
 11  -1.0 -  1.0i   0.833730025 - 0.988897706i  1.293454455*CIS(-0.870327425)
 12   0.0 -  1.0i   1.543080635 + 0.000000000i  1.543080635*CIS( 0.000000000)
 13   1.0 -  1.0i   0.833730025 + 0.988897706i  1.293454455*CIS( 0.870327425)
 14   5.0 +  0.0i   0.283662185 + 0.000000000i  0.283662185*CIS( 0.000000000)
 15   5.0 +  3.0i     2.8558150 +   9.6063834i   10.0218902*CIS(   1.2818340)
 16   0.0 +  3.0i    10.0676620 +   0.0000000i   10.0676620*CIS(   0.0000000)
 17  -5.0 +  3.0i     2.8558150 -   9.6063834i   10.0218902*CIS(  -1.2818340)
 18  -5.0 +  0.0i   0.283662185 + 0.000000000i  0.283662185*CIS( 0.000000000)
 19  -5.0 -  3.0i     2.8558150 +   9.6063834i   10.0218902*CIS(   1.2818340)
 20   0.0 -  3.0i    10.0676620 +   0.0000000i   10.0676620*CIS(   0.0000000)
 21  -5.0 -  3.0i     2.8558150 +   9.6063834i   10.0218902*CIS(   1.2818340)


Complex sine:  CSin = SIN(z)

                             SIN(z)
          z                rectangular             SIN^2(z)+COS^2(z)=1
     ------------  ---------------------------  ---------------------------
  1   0.0 +  0.0i   0.000000000 + 0.000000000i   1.000000000 + 0.000000000i
  2   0.5 +  0.5i   0.540612686 + 0.457304153i   1.000000000 + 0.000000000i
  3  -0.5 +  0.5i  -0.540612686 + 0.457304153i   1.000000000 + 0.000000000i
  4  -0.5 -  0.5i  -0.540612686 - 0.457304153i   1.000000000 + 0.000000000i
  5   0.5 -  0.5i   0.540612686 - 0.457304153i   1.000000000 + 0.000000000i
  6   1.0 +  0.0i   0.841470985 + 0.000000000i   1.000000000 + 0.000000000i
  7   1.0 +  1.0i   1.298457581 + 0.634963915i   1.000000000 + 0.000000000i
  8   0.0 +  1.0i   0.000000000 + 1.175201194i   1.000000000 + 0.000000000i
  9  -1.0 +  1.0i  -1.298457581 + 0.634963915i   1.000000000 + 0.000000000i
 10  -1.0 +  0.0i  -0.841470985 + 0.000000000i   1.000000000 + 0.000000000i
 11  -1.0 -  1.0i  -1.298457581 - 0.634963915i   1.000000000 + 0.000000000i
 12   0.0 -  1.0i   0.000000000 - 1.175201194i   1.000000000 + 0.000000000i
 13   1.0 -  1.0i   1.298457581 - 0.634963915i   1.000000000 + 0.000000000i
 14   5.0 +  0.0i  -0.958924275 + 0.000000000i   1.000000000 + 0.000000000i
 15   5.0 +  3.0i    -9.6541255 +   2.8416923i   1.000000000 + 0.000000000i
 16   0.0 +  3.0i     0.0000000 +  10.0178749i   1.000000000 + 0.000000000i
 17  -5.0 +  3.0i     9.6541255 +   2.8416923i   1.000000000 + 0.000000000i
 18  -5.0 +  0.0i   0.958924275 + 0.000000000i   1.000000000 + 0.000000000i
 19  -5.0 -  3.0i     9.6541255 -   2.8416923i   1.000000000 + 0.000000000i
 20   0.0 -  3.0i     0.0000000 -  10.0178749i   1.000000000 + 0.000000000i
 21  -5.0 -  3.0i     9.6541255 -   2.8416923i   1.000000000 + 0.000000000i


Complex tangent:  CTan = TAN(z)

                             TAN(z)                       TAN(z)
          z                rectangular                     polar
     ------------  ---------------------------  -----------------------------
  1   0.0 +  0.0i   0.000000000 + 0.000000000i  0.000000000*CIS( 0.000000000)
  2   0.5 +  0.5i   0.403896455 + 0.564083141i  0.693773837*CIS( 0.949397477)
  3  -0.5 +  0.5i  -0.403896455 + 0.564083141i  0.693773837*CIS( 2.192195177)
  4  -0.5 -  0.5i  -0.403896455 - 0.564083141i  0.693773837*CIS(-2.192195177)
  5   0.5 -  0.5i   0.403896455 - 0.564083141i  0.693773837*CIS(-0.949397477)
  6   1.0 +  0.0i   1.557407725 + 0.000000000i  1.557407725*CIS( 0.000000000)
  7   1.0 +  1.0i   0.271752585 + 1.083923327i  1.117470021*CIS( 1.325147658)
  8   0.0 +  1.0i   0.000000000 + 0.761594156i  0.761594156*CIS( 1.570796327)
  9  -1.0 +  1.0i  -0.271752585 + 1.083923327i  1.117470021*CIS( 1.816444995)
 10  -1.0 +  0.0i  -1.557407725 + 0.000000000i  1.557407725*CIS( 3.141592654)
 11  -1.0 -  1.0i  -0.271752585 - 1.083923327i  1.117470021*CIS(-1.816444995)
 12   0.0 -  1.0i   0.000000000 - 0.761594156i  0.761594156*CIS(-1.570796327)
 13   1.0 -  1.0i   0.271752585 - 1.083923327i  1.117470021*CIS(-1.325147658)
 14   5.0 +  0.0i  -3.380515006 + 0.000000000i  3.380515006*CIS( 3.141592654)
 15   5.0 +  3.0i  -0.002708236 + 1.004164711i  1.004168363*CIS( 1.573493324)
 16   0.0 +  3.0i   0.000000000 + 0.995054754i  0.995054754*CIS( 1.570796327)
 17  -5.0 +  3.0i   0.002708236 + 1.004164711i  1.004168363*CIS( 1.568099330)
 18  -5.0 +  0.0i   3.380515006 + 0.000000000i  3.380515006*CIS( 0.000000000)
 19  -5.0 -  3.0i   0.002708236 - 1.004164711i  1.004168363*CIS(-1.568099330)
 20   0.0 -  3.0i   0.000000000 - 0.995054754i  0.995054754*CIS(-1.570796327)
 21  -5.0 -  3.0i   0.002708236 - 1.004164711i  1.004168363*CIS(-1.568099330)


Complex hyperbolic cosine:  CCosh = COSH(z)

                             COSH(z)                      COSH(z)
          z                rectangular                     polar
     ------------  ---------------------------  -----------------------------
  1   0.0 +  0.0i   1.000000000 + 0.000000000i  1.000000000*CIS( 0.000000000)
  2   0.5 +  0.5i   0.989584883 + 0.249826398i  1.020632877*CIS( 0.247288622)
  3  -0.5 +  0.5i   0.989584883 - 0.249826398i  1.020632877*CIS(-0.247288622)
  4  -0.5 -  0.5i   0.989584883 + 0.249826398i  1.020632877*CIS( 0.247288622)
  5   0.5 -  0.5i   0.989584883 - 0.249826398i  1.020632877*CIS(-0.247288622)
  6   1.0 +  0.0i   1.543080635 + 0.000000000i  1.543080635*CIS( 0.000000000)
  7   1.0 +  1.0i   0.833730025 + 0.988897706i  1.293454455*CIS( 0.870327425)
  8   0.0 +  1.0i   0.540302306 + 0.000000000i  0.540302306*CIS( 0.000000000)
  9  -1.0 +  1.0i   0.833730025 - 0.988897706i  1.293454455*CIS(-0.870327425)
 10  -1.0 +  0.0i   1.543080635 + 0.000000000i  1.543080635*CIS( 0.000000000)
 11  -1.0 -  1.0i   0.833730025 + 0.988897706i  1.293454455*CIS( 0.870327425)
 12   0.0 -  1.0i   0.540302306 + 0.000000000i  0.540302306*CIS( 0.000000000)
 13   1.0 -  1.0i   0.833730025 - 0.988897706i  1.293454455*CIS(-0.870327425)
 14   5.0 +  0.0i    74.2099485 +   0.0000000i   74.2099485*CIS(   0.0000000)
 15   5.0 +  3.0i   -73.4672922 +  10.4715577i   74.2098143*CIS(   3.0000127)
 16   0.0 +  3.0i  -0.989992497 + 0.000000000i  0.989992497*CIS( 3.141592654)
 17  -5.0 +  3.0i   -73.4672922 -  10.4715577i   74.2098143*CIS(  -3.0000127)
 18  -5.0 +  0.0i    74.2099485 +   0.0000000i   74.2099485*CIS(   0.0000000)
 19  -5.0 -  3.0i   -73.4672922 +  10.4715577i   74.2098143*CIS(   3.0000127)
 20   0.0 -  3.0i  -0.989992497 + 0.000000000i  0.989992497*CIS( 3.141592654)
 21  -5.0 -  3.0i   -73.4672922 +  10.4715577i   74.2098143*CIS(   3.0000127)


Complex hyperbolic sine:  CSinh = SINH(z)

                             SINH(z)
          z                rectangular             COSH^2(z)-SINH^2(z)=1
     ------------  ---------------------------  ---------------------------
  1   0.0 +  0.0i   0.000000000 + 0.000000000i   1.000000000 + 0.000000000i
  2   0.5 +  0.5i   0.457304153 + 0.540612686i   1.000000000 + 0.000000000i
  3  -0.5 +  0.5i  -0.457304153 + 0.540612686i   1.000000000 + 0.000000000i
  4  -0.5 -  0.5i  -0.457304153 - 0.540612686i   1.000000000 + 0.000000000i
  5   0.5 -  0.5i   0.457304153 - 0.540612686i   1.000000000 + 0.000000000i
  6   1.0 +  0.0i   1.175201194 + 0.000000000i   1.000000000 + 0.000000000i
  7   1.0 +  1.0i   0.634963915 + 1.298457581i   1.000000000 + 0.000000000i
  8   0.0 +  1.0i   0.000000000 + 0.841470985i   1.000000000 + 0.000000000i
  9  -1.0 +  1.0i  -0.634963915 + 1.298457581i   1.000000000 + 0.000000000i
 10  -1.0 +  0.0i  -1.175201194 + 0.000000000i   1.000000000 + 0.000000000i
 11  -1.0 -  1.0i  -0.634963915 - 1.298457581i   1.000000000 + 0.000000000i
 12   0.0 -  1.0i   0.000000000 - 0.841470985i   1.000000000 + 0.000000000i
 13   1.0 -  1.0i   0.634963915 - 1.298457581i   1.000000000 + 0.000000000i
 14   5.0 +  0.0i    74.2032106 +   0.0000000i   1.000000000 + 0.000000000i
 15   5.0 +  3.0i   -73.4606217 +  10.4725085i   1.000000000 + 0.000000000i
 16   0.0 +  3.0i   0.000000000 + 0.141120008i   1.000000000 + 0.000000000i
 17  -5.0 +  3.0i    73.4606217 +  10.4725085i   1.000000000 + 0.000000000i
 18  -5.0 +  0.0i   -74.2032106 +   0.0000000i   1.000000000 + 0.000000000i
 19  -5.0 -  3.0i    73.4606217 -  10.4725085i   1.000000000 + 0.000000000i
 20   0.0 -  3.0i   0.000000000 - 0.141120008i   1.000000000 + 0.000000000i
 21  -5.0 -  3.0i    73.4606217 -  10.4725085i   1.000000000 + 0.000000000i


Complex hyperbolic tangent:  CTanh = TANH(z)

                             TANH(z)                      TANH(z)
          z                rectangular                     polar
     ------------  ---------------------------  -----------------------------
  1   0.0 +  0.0i   0.000000000 + 0.000000000i  0.000000000*CIS( 0.000000000)
  2   0.5 +  0.5i   0.564083141 + 0.403896455i  0.693773837*CIS( 0.621398850)
  3  -0.5 +  0.5i  -0.564083141 + 0.403896455i  0.693773837*CIS( 2.520193804)
  4  -0.5 -  0.5i  -0.564083141 - 0.403896455i  0.693773837*CIS(-2.520193804)
  5   0.5 -  0.5i   0.564083141 - 0.403896455i  0.693773837*CIS(-0.621398850)
  6   1.0 +  0.0i   0.761594156 + 0.000000000i  0.761594156*CIS( 0.000000000)
  7   1.0 +  1.0i   1.083923327 + 0.271752585i  1.117470021*CIS( 0.245648668)
  8   0.0 +  1.0i   0.000000000 + 1.557407725i  1.557407725*CIS( 1.570796327)
  9  -1.0 +  1.0i  -1.083923327 + 0.271752585i  1.117470021*CIS( 2.895943985)
 10  -1.0 +  0.0i  -0.761594156 + 0.000000000i  0.761594156*CIS( 3.141592654)
 11  -1.0 -  1.0i  -1.083923327 - 0.271752585i  1.117470021*CIS(-2.895943985)
 12   0.0 -  1.0i   0.000000000 - 1.557407725i  1.557407725*CIS(-1.570796327)
 13   1.0 -  1.0i   1.083923327 - 0.271752585i  1.117470021*CIS(-0.245648668)
 14   5.0 +  0.0i   0.999909204 + 0.000000000i  0.999909204*CIS( 0.000000000)
 15   5.0 +  3.0i   0.999912820 - 0.000025369i  0.999912820*CIS(-0.000025371)
 16   0.0 +  3.0i   0.000000000 - 0.142546543i  0.142546543*CIS(-1.570796327)
 17  -5.0 +  3.0i  -0.999912820 - 0.000025369i  0.999912820*CIS(-3.141567283)
 18  -5.0 +  0.0i  -0.999909204 + 0.000000000i  0.999909204*CIS( 3.141592654)
 19  -5.0 -  3.0i  -0.999912820 + 0.000025369i  0.999912820*CIS( 3.141567283)
 20   0.0 -  3.0i   0.000000000 + 0.142546543i  0.142546543*CIS( 1.570796327)
 21  -5.0 -  3.0i  -0.999912820 + 0.000025369i  0.999912820*CIS( 3.141567283)


Absolute value of complex number:  CAbs = ABS(z)

          z           ABS(z)
     ------------  ------------
  1   0.0 +  0.0i   0.000000000
  2   0.5 +  0.5i   0.707106781
  3  -0.5 +  0.5i   0.707106781
  4  -0.5 -  0.5i   0.707106781
  5   0.5 -  0.5i   0.707106781
  6   1.0 +  0.0i   1.000000000
  7   1.0 +  1.0i   1.414213562
  8   0.0 +  1.0i   1.000000000
  9  -1.0 +  1.0i   1.414213562
 10  -1.0 +  0.0i   1.000000000
 11  -1.0 -  1.0i   1.414213562
 12   0.0 -  1.0i   1.000000000
 13   1.0 -  1.0i   1.414213562
 14   5.0 +  0.0i   5.000000000
 15   5.0 +  3.0i   5.830951895
 16   0.0 +  3.0i   3.000000000
 17  -5.0 +  3.0i   5.830951895
 18  -5.0 +  0.0i   5.000000000
 19  -5.0 -  3.0i   5.830951895
 20   0.0 -  3.0i   3.000000000
 21  -5.0 -  3.0i   5.830951895

Complex integer power:  CIntPwr = z^n  (using DeMoivre's Theorem)

                               z^3                          z^3
          z                rectangular                     polar
     ------------  ---------------------------  -----------------------------
  1   0.0 +  0.0i           undefined
  2   0.5 +  0.5i  -0.250000000 + 0.250000000i  0.353553391*CIS( 2.356194490)
  3  -0.5 +  0.5i   0.250000000 + 0.250000000i  0.353553391*CIS( 0.785398163)
  4  -0.5 -  0.5i   0.250000000 - 0.250000000i  0.353553391*CIS(-0.785398163)
  5   0.5 -  0.5i  -0.250000000 - 0.250000000i  0.353553391*CIS(-2.356194490)
  6   1.0 +  0.0i   1.000000000 + 0.000000000i  1.000000000*CIS( 0.000000000)
  7   1.0 +  1.0i  -2.000000000 + 2.000000000i  2.828427125*CIS( 2.356194490)
  8   0.0 +  1.0i   0.000000000 - 1.000000000i  1.000000000*CIS(-1.570796327)
  9  -1.0 +  1.0i   2.000000000 + 2.000000000i  2.828427125*CIS( 0.785398163)
 10  -1.0 +  0.0i  -1.000000000 + 0.000000000i  1.000000000*CIS( 3.141592654)
 11  -1.0 -  1.0i   2.000000000 - 2.000000000i  2.828427125*CIS(-0.785398163)
 12   0.0 -  1.0i   0.000000000 + 1.000000000i  1.000000000*CIS( 1.570796327)
 13   1.0 -  1.0i  -2.000000000 - 2.000000000i  2.828427125*CIS(-2.356194490)
 14   5.0 +  0.0i   125.0000000 +   0.0000000i  125.0000000*CIS(   0.0000000)
 15   5.0 +  3.0i   -10.0000000 + 198.0000000i  198.2523644*CIS(   1.6212585)
 16   0.0 +  3.0i     0.0000000 -  27.0000000i   27.0000000*CIS(  -1.5707963)
 17  -5.0 +  3.0i    10.0000000 + 198.0000000i  198.2523644*CIS(   1.5203342)
 18  -5.0 +  0.0i  -125.0000000 +   0.0000000i  125.0000000*CIS(   3.1415927)
 19  -5.0 -  3.0i    10.0000000 - 198.0000000i  198.2523644*CIS(  -1.5203342)
 20   0.0 -  3.0i     0.0000000 +  27.0000000i   27.0000000*CIS(   1.5707963)
 21  -5.0 -  3.0i    10.0000000 - 198.0000000i  198.2523644*CIS(  -1.5203342)


Complex conjugate:  CConjugate = z*

                                 z*                           z*
          z                 rectangular                     polar
     ------------  ---------------------------  -----------------------------
  1   0.0 +  0.0i    0.00000000 +  0.00000000i   0.00000000*CIS(  0.00000000)
  2   0.5 +  0.5i    0.50000000 -  0.50000000i   0.70710678*CIS( -0.78539816)
  3  -0.5 +  0.5i   -0.50000000 -  0.50000000i   0.70710678*CIS( -2.35619449)
  4  -0.5 -  0.5i   -0.50000000 +  0.50000000i   0.70710678*CIS(  2.35619449)
  5   0.5 -  0.5i    0.50000000 +  0.50000000i   0.70710678*CIS(  0.78539816)
  6   1.0 +  0.0i    1.00000000 +  0.00000000i   1.00000000*CIS(  0.00000000)
  7   1.0 +  1.0i    1.00000000 -  1.00000000i   1.41421356*CIS( -0.78539816)
  8   0.0 +  1.0i    0.00000000 -  1.00000000i   1.00000000*CIS( -1.57079633)
  9  -1.0 +  1.0i   -1.00000000 -  1.00000000i   1.41421356*CIS( -2.35619449)
 10  -1.0 +  0.0i   -1.00000000 +  0.00000000i   1.00000000*CIS(  3.14159265)
 11  -1.0 -  1.0i   -1.00000000 +  1.00000000i   1.41421356*CIS(  2.35619449)
 12   0.0 -  1.0i    0.00000000 +  1.00000000i   1.00000000*CIS(  1.57079633)
 13   1.0 -  1.0i    1.00000000 +  1.00000000i   1.41421356*CIS(  0.78539816)
 14   5.0 +  0.0i    5.00000000 +  0.00000000i   5.00000000*CIS(  0.00000000)
 15   5.0 +  3.0i    5.00000000 -  3.00000000i   5.83095189*CIS( -0.54041950)
 16   0.0 +  3.0i    0.00000000 -  3.00000000i   3.00000000*CIS( -1.57079633)
 17  -5.0 +  3.0i   -5.00000000 -  3.00000000i   5.83095189*CIS( -2.60117315)
 18  -5.0 +  0.0i   -5.00000000 +  0.00000000i   5.00000000*CIS(  3.14159265)
 19  -5.0 -  3.0i   -5.00000000 +  3.00000000i   5.83095189*CIS(  2.60117315)
 20   0.0 -  3.0i    0.00000000 +  3.00000000i   3.00000000*CIS(  1.57079633)
 21  -5.0 -  3.0i   -5.00000000 +  3.00000000i   5.83095189*CIS(  2.60117315)


Complex square root:  CSqrt = SQRT(z)

                             SQRT(z)                     SQRT(z)
          z                   root 1                      root 2
     ------------  ---------------------------  ---------------------------
  1   0.0 +  0.0i   0.000000000 + 0.000000000i   0.000000000 + 0.000000000i
  2   0.5 +  0.5i   0.776886987 + 0.321797126i  -0.776886987 - 0.321797126i
  3  -0.5 +  0.5i   0.321797126 + 0.776886987i  -0.321797126 - 0.776886987i
  4  -0.5 -  0.5i   0.321797126 - 0.776886987i  -0.321797126 + 0.776886987i
  5   0.5 -  0.5i   0.776886987 - 0.321797126i  -0.776886987 + 0.321797126i
  6   1.0 +  0.0i   1.000000000 + 0.000000000i  -1.000000000 + 0.000000000i
  7   1.0 +  1.0i   1.098684113 + 0.455089861i  -1.098684113 - 0.455089861i
  8   0.0 +  1.0i   0.707106781 + 0.707106781i  -0.707106781 - 0.707106781i
  9  -1.0 +  1.0i   0.455089861 + 1.098684113i  -0.455089861 - 1.098684113i
 10  -1.0 +  0.0i   0.000000000 + 1.000000000i   0.000000000 - 1.000000000i
 11  -1.0 -  1.0i   0.455089861 - 1.098684113i  -0.455089861 + 1.098684113i
 12   0.0 -  1.0i   0.707106781 - 0.707106781i  -0.707106781 + 0.707106781i
 13   1.0 -  1.0i   1.098684113 - 0.455089861i  -1.098684113 + 0.455089861i
 14   5.0 +  0.0i   2.236067977 + 0.000000000i  -2.236067977 + 0.000000000i
 15   5.0 +  3.0i   2.327117519 + 0.644574237i  -2.327117519 - 0.644574237i
 16   0.0 +  3.0i   1.224744871 + 1.224744871i  -1.224744871 - 1.224744871i
 17  -5.0 +  3.0i   0.644574237 + 2.327117519i  -0.644574237 - 2.327117519i
 18  -5.0 +  0.0i   0.000000000 + 2.236067977i   0.000000000 - 2.236067977i
 19  -5.0 -  3.0i   0.644574237 - 2.327117519i  -0.644574237 + 2.327117519i
 20   0.0 -  3.0i   1.224744871 - 1.224744871i  -1.224744871 + 1.224744871i
 21  -5.0 -  3.0i   0.644574237 - 2.327117519i  -0.644574237 + 2.327117519i


The three cube roots of -1+i:  (-1+i)^(1/3)
(See Schaum's Outline Series "Complex Variables", 1964, p. 18, problem 29.)

                            z^(1/3)                      z^(1/3)
          z                rectangular                     polar
     ------------  ---------------------------  -----------------------------
  0  -1.0 +  1.0i   0.793700526 + 0.793700526i  1.122462048*CIS( 0.785398163)
  1  -1.0 +  1.0i  -1.084215081 + 0.290514556i  1.122462048*CIS( 2.879793266)
  2  -1.0 +  1.0i   0.290514556 - 1.084215081i  1.122462048*CIS(-1.308996939)


Complex Bessel function:  CI0 = I0(z)

                               I0(z)                        I0(z)
          z                rectangular                     polar
     ------------  ---------------------------  -----------------------------
  1   0.0 +  0.0i   1.000000000 + 0.000000000i  1.000000000*CIS( 0.000000000)
  2   0.5 +  0.5i   0.996094174 + 0.124945749i  1.003899917*CIS( 0.124783947)
  3  -0.5 +  0.5i   0.996094174 - 0.124945749i  1.003899917*CIS(-0.124783947)
  4  -0.5 -  0.5i   0.996094174 + 0.124945749i  1.003899917*CIS( 0.124783947)
  5   0.5 -  0.5i   0.996094174 - 0.124945749i  1.003899917*CIS(-0.124783947)
  6   1.0 +  0.0i   1.266065878 + 0.000000000i  1.266065878*CIS( 0.000000000)
  7   1.0 +  1.0i   0.937608477 + 0.496529948i  1.060967316*CIS( 0.487023340)
  8   0.0 +  1.0i   0.765197687 + 0.000000000i  0.765197687*CIS( 0.000000000)
  9  -1.0 +  1.0i   0.937608477 - 0.496529948i  1.060967316*CIS(-0.487023340)
 10  -1.0 +  0.0i   1.266065878 + 0.000000000i  1.266065878*CIS( 0.000000000)
 11  -1.0 -  1.0i   0.937608477 + 0.496529948i  1.060967316*CIS( 0.487023340)
 12   0.0 -  1.0i   0.765197687 + 0.000000000i  0.765197687*CIS( 0.000000000)
 13   1.0 -  1.0i   0.937608477 - 0.496529948i  1.060967316*CIS(-0.487023340)
 14   5.0 +  0.0i    27.2398718 +   0.0000000i   27.2398718*CIS(   0.0000000)
 15   5.0 +  3.0i   -22.7714931 +  10.3008933i   24.9929850*CIS(   2.7167786)
 16   0.0 +  3.0i  -0.260051955 + 0.000000000i  0.260051955*CIS( 3.141592654)
 17  -5.0 +  3.0i   -22.7714931 -  10.3008933i   24.9929850*CIS(  -2.7167786)
 18  -5.0 +  0.0i    27.2398718 +   0.0000000i   27.2398718*CIS(   0.0000000)
 19  -5.0 -  3.0i   -22.7714931 +  10.3008933i   24.9929850*CIS(   2.7167786)
 20   0.0 -  3.0i  -0.260051955 + 0.000000000i  0.260051955*CIS( 3.141592654)
 21  -5.0 -  3.0i   -22.7714931 +  10.3008933i   24.9929850*CIS(   2.7167786)


Complex Bessel function:  CJ0 = J0(z)

                               J0(z)                        J0(z)
          z                rectangular                     polar
     ------------  ---------------------------  -----------------------------
  1   0.0 +  0.0i   1.000000000 + 0.000000000i  1.000000000*CIS( 0.000000000)
  2   0.5 +  0.5i   0.996094174 - 0.124945749i  1.003899917*CIS(-0.124783947)
  3  -0.5 +  0.5i   0.996094174 + 0.124945749i  1.003899917*CIS( 0.124783947)
  4  -0.5 -  0.5i   0.996094174 - 0.124945749i  1.003899917*CIS(-0.124783947)
  5   0.5 -  0.5i   0.996094174 + 0.124945749i  1.003899917*CIS( 0.124783947)
  6   1.0 +  0.0i   0.765197687 + 0.000000000i  0.765197687*CIS( 0.000000000)
  7   1.0 +  1.0i   0.937608477 - 0.496529948i  1.060967316*CIS(-0.487023340)
  8   0.0 +  1.0i   1.266065878 + 0.000000000i  1.266065878*CIS( 0.000000000)
  9  -1.0 +  1.0i   0.937608477 + 0.496529948i  1.060967316*CIS( 0.487023340)
 10  -1.0 +  0.0i   0.765197687 + 0.000000000i  0.765197687*CIS( 0.000000000)
 11  -1.0 -  1.0i   0.937608477 - 0.496529948i  1.060967316*CIS(-0.487023340)
 12   0.0 -  1.0i   1.266065878 + 0.000000000i  1.266065878*CIS( 0.000000000)
 13   1.0 -  1.0i   0.937608477 + 0.496529948i  1.060967316*CIS( 0.487023340)
 14   5.0 +  0.0i  -0.177596771 + 0.000000000i  0.177596771*CIS( 3.141592654)
 15   5.0 +  3.0i  -0.826710665 + 3.243219941i  3.346927862*CIS( 1.820385436)
 16   0.0 +  3.0i   4.880792586 + 0.000000000i  4.880792586*CIS( 0.000000000)
 17  -5.0 +  3.0i  -0.826710665 - 3.243219941i  3.346927862*CIS(-1.820385436)
 18  -5.0 +  0.0i  -0.177596771 + 0.000000000i  0.177596771*CIS( 3.141592654)
 19  -5.0 -  3.0i  -0.826710665 + 3.243219941i  3.346927862*CIS( 1.820385436)
 20   0.0 -  3.0i   4.880792586 + 0.000000000i  4.880792586*CIS( 0.000000000)
 21  -5.0 -  3.0i  -0.826710665 + 3.243219941i  3.346927862*CIS( 1.820385436)


Removing "Fuzz" from real numbers for zero test:

  Before:  -0.000000000000032 + 0.000000000000077i
   After:   0.000000000000000 + 0.000000000000000i

  Before:  -0.000000000000032*CIS( 3.141592653589793)
   After:   0.000000000000000*CIS( 0.000000000000000)


Miscellaneous:  FixAngle -- keep angle in interval (-PI..PI)

     radians FixAngle
    -------- --------
 -4 -6.28319  0.00000
 -3 -4.71239  1.57080
 -2 -3.14159 -3.14159
 -1 -1.57080 -1.57080
  0  0.00000  0.00000
  1  1.57080  1.57080
  2  3.14159  3.14159
  3  4.71239 -1.57080
  4  6.28319  0.00000
  5  7.85398  1.57080
  6  9.42478  3.14159
  7 10.99557 -1.57080
  8 12.56637  0.00000


Real power function:  Pwr = x^y

        x        y         x^y
    -------- -------- ------------
     2.10000 -2.50000 0.156477451
     2.10000  2.50000 6.390697145
     1.40000  8.90000 5.066558830
     0.00000  2.00000 0.000000000
     4.20000  0.00000 1.000000000

