math::complexnumbers - Straightforward complex number package

       The package implements all or most basic operations and elementary functions.

       Thearithmeticoperationsare:::math::complexnumbers::+z1z2
              Add the two arguments and return the resulting complex number

              complex z1 (in)
                     First argument in the summation

              complex z2 (in)
                     Second argument in the summation

       ::math::complexnumbers::-z1z2
              Subtract the second argument from the first and return the resulting complex number. If  there  is
              only one argument, the opposite of z1 is returned (i.e. -z1)

              complex z1 (in)
                     First argument in the subtraction

              complex z2 (in)
                     Second argument in the subtraction (optional)

       ::math::complexnumbers::*z1z2
              Multiply the two arguments and return the resulting complex number

              complex z1 (in)
                     First argument in the multiplication

              complex z2 (in)
                     Second argument in the multiplication

       ::math::complexnumbers::/z1z2
              Divide the first argument by the second and return the resulting complex number

              complex z1 (in)
                     First argument (numerator) in the division

              complex z2 (in)
                     Second argument (denominator) in the division

       ::math::complexnumbers::conjz1
              Return the conjugate of the given complex number

              complex z1 (in)
                     Complex number in question

       Conversion/inquiryprocedures:::math::complexnumbers::realz1
              Return the real part of the given complex number

              complex z1 (in)
                     Complex number in question

       ::math::complexnumbers::imagz1
              Return the imaginary part of the given complex number

              complex z1 (in)
                     Complex number in question

       ::math::complexnumbers::modz1
              Return the modulus of the given complex number

              complex z1 (in)
                     Complex number in question

       ::math::complexnumbers::argz1
              Return the argument ("angle" in radians) of the given complex number

              complex z1 (in)
                     Complex number in question

       ::math::complexnumbers::complexrealimag
              Construct the complex number "real + imag*i" and return it

              float real (in)
                     The real part of the new complex number

              float imag (in)
                     The imaginary part of the new complex number

       ::math::complexnumbers::tostringz1
              Convert the complex number to the form "real + imag*i" and return the string

              float complex (in)
                     The complex number to be converted

       Elementaryfunctions:::math::complexnumbers::expz1
              Calculate the exponential for the given complex argument and return the result

              complex z1 (in)
                     The complex argument for the function

       ::math::complexnumbers::sinz1
              Calculate the sine function for the given complex argument and return the result

              complex z1 (in)
                     The complex argument for the function

       ::math::complexnumbers::cosz1
              Calculate the cosine function for the given complex argument and return the result

              complex z1 (in)
                     The complex argument for the function

       ::math::complexnumbers::tanz1
              Calculate the tangent function for the given complex argument and return the result

              complex z1 (in)
                     The complex argument for the function

       ::math::complexnumbers::logz1
              Calculate  the  (principle  value  of the) logarithm for the given complex argument and return the
              result

              complex z1 (in)
                     The complex argument for the function

       ::math::complexnumbers::sqrtz1
              Calculate the (principle value of the) square root for the given complex argument and  return  the
              result

              complex z1 (in)
                     The complex argument for the function

       ::math::complexnumbers::powz1z2
              Calculate "z1 to the power of z2" and return the result

              complex z1 (in)
                     The complex number to be raised to a power

              complex z2 (in)
                     The complex power to be used

       This  document,  and  the package it describes, will undoubtedly contain bugs and other problems.  Please
       report   such    in    the    category    math::complexnumbers    of    the    TcllibTrackers
       [http://core.tcl.tk/tcllib/reportlist].   Please  also report any ideas for enhancements you may have for
       either package and/or documentation.

       When proposing code changes, please provide unifieddiffs, i.e the output of diff-u.

       Note further that attachments are strongly preferred over inlined patches. Attachments  can  be  made  by
       going  to the Edit form of the ticket immediately after its creation, and then using the left-most button
       in the secondary navigation bar.

       Mathematics

       Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>

tcllib                                                1.0.3                           math::complexnumbers(3tcl)

       The  mathematical  module  complexnumbers provides a straightforward implementation of complex numbers in
       pure Tcl. The philosophy is that the user knows he or she is dealing with complex numbers in an  abstract
       way and wants as high a performance as can be had within the limitations of an interpreted language.

       Therefore the procedures defined in this package assume that the arguments are valid (representations of)
       "complex numbers", that is, lists of two numbers defining the real and imaginary part of a complex number
       (though this is a mere detail: rely on the complex command to construct a valid number.)

       Most  procedures implement the basic arithmetic operations or elementary functions whereas several others
       convert to and from different representations:

                  set z [complex 0 1]
                  puts "z = [tostring $z]"
                  puts "z**2 = [* $z $z]

       would result in:

                  z = i
                  z**2 = -1

       complex numbers, math

       math::complexnumbers - Straightforward complex number package

       package require Tcl8.59

       package require math::complexnumbers?1.0.3?::math::complexnumbers::+z1z2::math::complexnumbers::-z1z2::math::complexnumbers::*z1z2::math::complexnumbers::/z1z2::math::complexnumbers::conjz1::math::complexnumbers::realz1::math::complexnumbers::imagz1::math::complexnumbers::modz1::math::complexnumbers::argz1::math::complexnumbers::complexrealimag::math::complexnumbers::tostringz1::math::complexnumbers::expz1::math::complexnumbers::sinz1::math::complexnumbers::cosz1::math::complexnumbers::tanz1::math::complexnumbers::logz1::math::complexnumbers::sqrtz1::math::complexnumbers::powz1z2

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