Working with complex numbers

Working with complex numbers

How to:

C++ has a built-in library <complex> that eases working with complex numbers. Here’s a quick look:

#include <iostream>
#include <complex>

int main() {
    std::complex<double> num1(2.0, 3.0); // Creates a complex number (2 + 3i)
    std::complex<double> num2(3.0, 4.0); // Another complex number (3 + 4i)

    // Addition
    std::complex<double> result = num1 + num2;
    std::cout << "Addition result: " << result << std::endl; // (5 + 7i)

    // Multiplication
    result = num1 * num2;
    std::cout << "Multiplication result: " << result << std::endl; // (-6 + 17i)

    // Conjugate
    result = std::conj(num1);
    std::cout << "Conjugate of num1: " << result << std::endl; // (2 - 3i)
    return 0;

Deep Dive

Complex numbers have a rich history, first cropping up in solutions to cubic equations in the 16th century. They’re essential in many fields, not just programming. Within computer science, complex numbers help in algorithms that require a two-dimensional number space, like the Fast Fourier Transform (FFT).

While C++’s <complex> library is standard, alternatives exist in other languages, like Python’s complex data type or JavaScript’s math libraries. The <complex> library itself provides comprehensive functionality, including trigonometric, exponential, and logarithmic operations tailored for complex numbers.

When programming these numbers, it’s key to grasp the underlying mathematics to prevent inaccuracies and understand operations like complex conjugation, which flips the sign of the imaginary part, or the implications of Euler’s formula relating complex exponentials to trigonometric functions.

See Also