C Programming/complex.h

Summary

complex.h is a header file that defines functionality for complex arithmetic. These functions use the built-in type complex which was introduced with the C99 revision of C.

This header should not be confused with the C++ standard library header <complex>, which implements complex numbers in a completely different way (as a template class, complex<T>).

Macros

Universal macro:

• complex - alias of _Complex
• _Complex_I - constant, which has type "const float _Complex" and value of imaginary unit I, I*I=-1

Defined only for `C99 Annex G`-compatible compiler modes - native support of imaginary types (it is very rare because Annex G is mathematically incorrect):

• imaginary - alias of _Imaginary
• _Imaginary_I Expands to a constant expression of type const float _Imaginary with the value of the imaginary unit.

Universal alias of I:

• I - alias of _Imaginary_I if it is defined else - alias of _Complex_I

Application may undefine complex, imaginary, and I macros if they interfere with internal values.

Functions Overview

Each function declared in complex.h has three versions, each of which works with a different floating-point type (double, float and long double). Only the double version of each function is listed here; to use the float (or long double) version, append an f (or an l, respectively) to the function's name (e.g., cabsf and cabsl).

Note that all angles are in radians.

Basic operations

cabs	computes absolute value
carg	computes argument of a complex number
cimag	computes imaginary part of a complex number
creal	computes real part of a complex number
conj	computes complex conjugate
cproj	computes complex projection into the Riemann sphere

Exponentiation operations

cexp	computes complex exponential
clog	computes complex logarithm
csqrt	computes complex square root
cpow	computes complex power

Trigonometric operations

csin	computes complex sine
ccos	computes complex cosine
ctan	computes complex tangent
casin	computes complex arc sine
cacos	computes complex arc cosine
catan	computes complex arc tangent

Hyperbolic operations

csinh	computes complex hyperbolic sine
ccosh	computes complex hyperbolic cosine
ctanh	computes complex hyperbolic tangent
casinh	computes complex hyperbolic arc sine
cacosh	computes complex hyperbolic arc cosine
catanh	computes complex hyperbolic arc tangent