Complex numbers in MATLAB

Introduction

Complex numbers let us work with numbers that have a real part and an imaginary part. They help solve problems that normal numbers can't handle.

When you need to represent signals in engineering that have both magnitude and phase.

When solving equations that have no real solutions, like square roots of negative numbers.

When working with electrical circuits involving alternating current (AC).

When analyzing waves or oscillations in physics.

When performing Fourier transforms in data processing.

Syntax

MATLAB

z = a + b*i;
% or
z = complex(a, b);

Here, a is the real part and b is the imaginary part.

In MATLAB, i or j represents the imaginary unit (√-1).

Examples

This creates a complex number with real part 3 and imaginary part 4.

MATLAB

z1 = 3 + 4i;

This creates a complex number with real part 5 and imaginary part -2 using the complex function.

MATLAB

z2 = complex(5, -2);

You can also use j instead of i for the imaginary unit.

MATLAB

z3 = 7 - 3j;

Sample Program

This program creates two complex numbers, adds them, multiplies them, and prints the results showing real and imaginary parts.

MATLAB

a = 2 + 3i;
b = complex(1, -1);
sum = a + b;
product = a * b;

fprintf('Sum: %.2f + %.2fi\n', real(sum), imag(sum));
fprintf('Product: %.2f + %.2fi\n', real(product), imag(product));

Important Notes

Use real(z) and imag(z) to get the real and imaginary parts of a complex number.

Be careful not to overwrite i or j as variables, or MATLAB will not recognize them as imaginary units.

Complex arithmetic follows special rules different from real numbers, but MATLAB handles them automatically.

Summary

Complex numbers have a real and an imaginary part.

Use i or j to write imaginary parts in MATLAB.

MATLAB provides functions to create and work with complex numbers easily.