qcomplex(n) [osx man page]

```math::complexnumbers(n) 					 Tcl Math Library					   math::complexnumbers(n)

__________________________________________________________________________________________________________________________________________________

NAME
math::complexnumbers - Straightforward complex number package

SYNOPSIS
package require Tcl  8.3

package require math::complexnumbers  ?1.0.2?

::math::complexnumbers::+ z1 z2

::math::complexnumbers::- z1 z2

::math::complexnumbers::* z1 z2

::math::complexnumbers::/ z1 z2

::math::complexnumbers::conj z1

::math::complexnumbers::real z1

::math::complexnumbers::imag z1

::math::complexnumbers::mod z1

::math::complexnumbers::arg z1

::math::complexnumbers::complex real imag

::math::complexnumbers::tostring z1

::math::complexnumbers::exp z1

::math::complexnumbers::sin z1

::math::complexnumbers::cos z1

::math::complexnumbers::tan z1

::math::complexnumbers::log z1

::math::complexnumbers::sqrt z1

::math::complexnumbers::pow z1 z2

_________________________________________________________________

DESCRIPTION
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  limita-
tions 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  con-
struct a valid number.)

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

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

would result in:

z = i
z**2 = -1

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

The arithmetic operations are:

::math::complexnumbers::+ z1 z2
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::- z1 z2
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::* z1 z2
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::/ z1 z2
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::conj z1
Return the conjugate of the given complex number

complex z1 (in)
Complex number in question

Conversion/inquiry procedures:

::math::complexnumbers::real z1
Return the real part of the given complex number

complex z1 (in)
Complex number in question

::math::complexnumbers::imag z1
Return the imaginary part of the given complex number

complex z1 (in)
Complex number in question

::math::complexnumbers::mod z1
Return the modulus of the given complex number

complex z1 (in)
Complex number in question

::math::complexnumbers::arg z1
Return the argument ("angle" in radians) of the given complex number

complex z1 (in)
Complex number in question

::math::complexnumbers::complex real imag
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::tostring z1
Convert the complex number to the form "real + imag*i" and return the string

float complex (in)
The complex number to be converted

Elementary functions:

::math::complexnumbers::exp z1
Calculate the exponential for the given complex argument and return the result

complex z1 (in)
The complex argument for the function

::math::complexnumbers::sin z1
Calculate the sine function for the given complex argument and return the result

complex z1 (in)
The complex argument for the function

::math::complexnumbers::cos z1
Calculate the cosine function for the given complex argument and return the result

complex z1 (in)
The complex argument for the function

::math::complexnumbers::tan z1
Calculate the tangent function for the given complex argument and return the result

complex z1 (in)
The complex argument for the function

::math::complexnumbers::log z1
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::sqrt z1
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::pow z1 z2
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

BUGS, IDEAS, FEEDBACK
This  document, and the package it describes, will undoubtedly contain bugs and other problems.	Please report such in the category math ::
complexnumbers of the Tcllib SF Trackers [http://sourceforge.net/tracker/?group_id=12883].  Please also report any ideas  for  enhancements
you may have for either package and/or documentation.

KEYWORDS
complex numbers, math

CATEGORY
Mathematics