# <complex.h>

**[<complex.h>](https://en.cppreference.com/w/c/header/complex)** provides `_Complex` type (C99) and complex number functions: magnitude (`cabs`), phase (`carg`), conjugate (`conj`), and full trigonometric/exponential support. Arithmetic operators work natively on complex types.

Use it for signal processing, electrical engineering, and quantum mechanics where complex arithmetic is essential.

## Example

This example performs complex arithmetic and demonstrates Euler's formula relationship.

```c
// compile: gcc -std=c99 -o complexexample complexexample.c -lm
// run: ./complexexample
// description: complex arithmetic and magnitude calculation

#include <complex.h>
#include <math.h>
#include <stdio.h>

int main() {
    double complex z = 3.0 + 4.0 * I;
    
    printf("|z| = %.1f\n", cabs(z));
    printf("arg(z) = %.4f rad\n", carg(z));
    printf("conj(z) = %.1f%+.1fi\n", creal(conj(z)), cimag(conj(z)));
    
    double complex euler = cexp(I * M_PI);
    printf("e^(i*pi) ≈ %.6f%+.6fi\n", creal(euler), cimag(euler));
    
    return 0;
}
```