Complex Numbers in C++

1. Complex Numbers Library in C++
2. Complex Functions in C++
3. Use the Complex Numbers Library in C++

The imaginary number "i", which is denoted by the lowercase letter "i" (or sometimes by the symbol √-1), is a mathematical constant that’s defined as the square root of a negative one.

The imaginary number "i" is used in C++ code to represent complex numbers. Complex numbers are composed of two parts, a real part and an imaginary part, and they’re written in the form a+bi, where a is the real part, and b is the imaginary part.

In this post, we will go over the fundamentals of using complex numbers in C++.

Complex Numbers Library in C++

This library is a collection of complex number classes and functions for C++. It provides the following features:

• Complex numbers with arbitrary precision.
• Complex numbers with arbitrary precision and in polar form.
• Complex number arithmetic operations (addition, subtraction, multiplication, division).
• Complex number conversion between polar and rectangular forms.
• Complex number inversion (finding the real part of a complex number).
• Real part extraction from a complex number.

Complex Functions in C++

Complex functions in C++ are a set of functions that perform mathematical operations on complex numbers. They can be used in solving complex problems and equations.

Moreover, Complex functions in C++ are not just the more complex versions of the simple functions. They are different from their counterparts in that they can accept a variable number of arguments and return a value with a variable number of components.

It is important to note that these functions are not part of the standard C++ library but are usually implemented as an extension library.

Let’s discuss some of the C++ complex functions in detail.

• The sqrt() function is used to calculate the square root of a number.
• The abs() function is used to find the absolute value of a number.
• The norm() function calculates the magnitude of a vector.
• The polar() functions calculate the magnitude of a vector in polar coordinates.
• The proj() functions project a point onto a plane defined by two points.
• The arg(x,y) function returns the angle from one point to another.

Use the Complex Numbers Library in C++

Let’s discuss how to use the Complex Numbers library in C++.

Example Code:

#include <complex>
#include <iostream>
using namespace std;

int main() {
  complex<double> demo(3.0, 6.0);
  cout << "Real Number" << real(demo) << endl;
  cout << "Imaginary Number " << imag(demo) << endl;
  return 0;
}

Output:

Real Number3
Imaginary Number 6

Click here to check the live demonstration of the code above.