11.3 Complex Data Types

Complex numbers can include both a real part and an imaginary part. The numeric constants covered above have real-numbered values. An imaginary-valued constant is an ordinary real-valued constant followed by ‘i’.

To declare numeric variables as complex, use the _Complex keyword.⁴ The standard C complex data types are floating point,

_Complex float foo;
_Complex double bar;
_Complex long double quux;

but GNU C supports integer complex types as well.

Since _Complex is a keyword just like float and double and long, the keywords can appear in any order, but the order shown above seems most logical.

GNU C supports constants for complex values; for instance, 4.0 + 3.0i has the value 4 + 3i as type _Complex double. See Imaginary Constants.

To pull the real and imaginary parts of the number back out, GNU C provides the keywords __real__ and __imag__:

_Complex double foo = 4.0 + 3.0i;

double a = __real__ foo; /* a is now 4.0. */
double b = __imag__ foo; /* b is now 3.0. */

Standard C does not include these keywords, and instead relies on functions defined in complex.h for accessing the real and imaginary parts of a complex number: crealf, creal, and creall extract the real part of a float, double, or long double complex number, respectively; cimagf, cimag, and cimagl extract the imaginary part.

GNU C also defines ‘~’ as an operator for complex conjugation, which means negating the imaginary part of a complex number:

_Complex double foo = 4.0 + 3.0i;
_Complex double bar = ~foo; /* bar is now 4 - 3i. */

For standard C compatibility, you can use the appropriate library function: conjf, conj, or confl.