# <complex>

**[<complex>](https://en.cppreference.com/w/cpp/header/complex)** provides `std::complex<T>` for complex numbers with arithmetic operations, trigonometric functions, and conversions. It's useful for signal processing, control theory, and wave simulations.

Operations like `abs()`, `arg()`, `conj()`, `polar()` work on complex numbers just as you'd expect, and they compose with `<cmath>` functions.

## Example

This example performs arithmetic on complex numbers, calculates magnitude and phase, and constructs a complex number from polar form.

```cpp
// compile: g++ -std=c++11 -o complexexample complexexample.cpp
// run: ./complexexample
// description: complex arithmetic and polar form

#include <complex>
#include <iostream>
#include <cmath>

int main() {
    std::complex<double> z1(3, 4);
    std::complex<double> z2(1, 2);
    
    auto product = z1 * z2;
    std::cout << "product: " << product << "\n";
    
    std::cout << "magnitude of z1: " << std::abs(z1) << "\n";
    std::cout << "phase of z1: " << std::arg(z1) << " radians\n";
    
    auto polar = std::polar(2.0, M_PI / 4);
    std::cout << "polar(2, pi/4): " << polar << "\n";
    
    return 0;
}
```