Conjugate of a Complex number

Definition

A complex number having an equal real part and an equal imaginary part in magnitude but opposite in sign is called the complex conjugate of a complex number.

Introduction

Let’s learn what the conjugate of a complex number really is in detail. A complex number may have following two similarities with another complex number.

1. The real part of a complex number is equal to the real part of another complex number.
2. The imaginary part of a complex number in magnitude is equal to the magnitude of another complex number but they both have opposite signs.

Now, a complex number is called the conjugate of another complex number, and vice-versa.

Let’s assume that $a$ and $b$ denote two real numbers. A complex number can be written in the following two forms popularly in terms of $a$ and $b$, where $i$ denotes an imaginary unit.

1. $a+ib$
2. $a-ib$

The real part of both complex numbers are $a$ and they both are equal in magnitude. Similarly, the imaginary part of both complex numbers are $b$ and they both are equal in magnitude but they have opposite signs.

So, the complex number $a+ib$ is called the conjugate of complex number $a-ib$. Similarly, the complex number $a-ib$ is called the conjugate of complex number $a+ib$.

So, you can use any one of them to represent the complex conjugate of a complex number.

Now, let’s learn more about the complex conjugate of a complex number in detail.

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