20.9 Complex Numbers

ISO C99 introduces support for complex numbers in C. This is done with a new type qualifier, complex. It is a keyword if and only if complex.h has been included. There are three complex types, corresponding to the three real types: float complex, double complex, and long double complex.

Likewise, on machines that have support for _FloatN or _FloatNx enabled, the complex types _FloatN complex and _FloatNx complex are also available if complex.h has been included; see Mathematics.

To construct complex numbers you need a way to indicate the imaginary part of a number. There is no standard notation for an imaginary floating point constant. Instead, complex.h defines two macros that can be used to create complex numbers.

Macro: const float complex _Complex_I

This macro is a representation of the complex number “0+1i”. Multiplying a real floating-point value by _Complex_I gives a complex number whose value is purely imaginary. You can use this to construct complex constants:

3.0 + 4.0i = 3.0 + 4.0 * _Complex_I

Note that _Complex_I * _Complex_I has the value -1, but the type of that value is complex.

_Complex_I is a bit of a mouthful. complex.h also defines a shorter name for the same constant.

Macro: const float complex I

This macro has exactly the same value as _Complex_I. Most of the time it is preferable. However, it causes problems if you want to use the identifier I for something else. You can safely write

#include <complex.h>
#undef I

if you need I for your own purposes. (In that case we recommend you also define some other short name for _Complex_I, such as J.)