Complex number arithmetic - cppreference.com (original) (raw)

Complex number arithmetic

The C programming language, as of C99, supports complex number math with the three built-in types double _Complex, float _Complex, and long double _Complex (see _Complex). When the header <complex.h> is included, the three complex number types are also accessible as double complex, float complex, long double complex.

In addition to the complex types, the three imaginary types may be supported: double _Imaginary, float _Imaginary, and long double _Imaginary (see _Imaginary). When the header <complex.h> is included, the three imaginary types are also accessible as double imaginary, float imaginary, and long double imaginary.

Standard arithmetic operators +, -, *, / can be used with real, complex, and imaginary types in any combination.

[edit] Notes

The following function names are potentially(since C23) reserved for future addition to <complex.h> and are not available for use in the programs that include that header: cerf, cerfc, cexp2, cexpm1, clog10, clog1p, clog2, clgamma, ctgamma, csinpi, ccospi, ctanpi, casinpi, cacospi, catanpi, ccompoundn, cpown, cpowr, crootn, crsqrt, cexp10m1, cexp10, cexp2m1, clog10p1, clog2p1, clogp1(since C23), along with their -f and -l suffixed variants.

Although the C standard names the inverse hyperbolic with "complex arc hyperbolic sine" etc., the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct names are "complex inverse hyperbolic sine" etc. Some authors use "complex area hyperbolic sine" etc.

A complex or imaginary number is infinite if one of its parts is infinite, even if the other part is NaN.

A complex or imaginary number is finite if both parts are neither infinities nor NaNs.

A complex or imaginary number is a zero if both parts are positive or negative zeroes.

While MSVC does provide a <complex.h> header, it does not implement complex numbers as native types, but as structs, which are incompatible with standard C complex types and do not support the +, -, *, / operators.

[edit] Example

#include <complex.h> #include <stdio.h> #include <tgmath.h>   int main(void) { double complex z1 = I * I; // imaginary unit squared printf("I * I = %.1f%+.1fi\n", creal(z1), cimag(z1));   double complex z2 = pow(I, 2); // imaginary unit squared printf("pow(I, 2) = %.1f%+.1fi\n", creal(z2), cimag(z2));   double PI = acos(-1); double complex z3 = exp(I * PI); // Euler's formula printf("exp(IPI) = %.1f%+.1fi\n", creal(z3), cimag(z3));   double complex z4 = 1 + 2 * I, z5 = 1 - 2 * I; // conjugates printf("(1+2i)(1-2i) = %.1f%+.1fi\n", creal(z4 * z5), cimag(z4 * z5)); }

Output:

I * I = -1.0+0.0i pow(I, 2) = -1.0+0.0i exp(IPI) = -1.0+0.0i (1+2i)(1-2i) = 5.0+0.0i

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