Question

What is the complex conjugate of a complex number ?

Answer 1

Hint: In this question, we need to explain the complex conjugate of the complex number. Mathematically, complex numbers are represented as \[x\ + \ iy\] where \[x\] and \[y\] are the real numbers and here \[i\] is an imaginary number. The set of complex numbers is basically denoted by \[C\] . Conjugate of the number is nothing but it is formed by changing the sign of one of the terms. Let us explain the complex conjugate of a complex number with an example.

Complete step-by-step answer:
Complex number consists of two parts namely the real part and the imaginary part. It is the sum of real numbers and imaginary numbers. In the general form \[x\ + \ iy\] . Here \[x\] is the real part and \[iy\] is the imaginary part . Imaginary part is denoted by Im(z) and the real part is denoted by Re(z). If only the sign of the imaginary part of the complex number differs then, they are known as a complex conjugate of each other, that is the complex number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
The complex conjugate of a complex number \[z\] is represented as \[z^{*}\] .
Let us consider an example for complex numbers.
\[z=4+3i\]
Here \[4\] is the real part and \[3i\] is the imaginary part .
The complex conjugate of \[4+3i\] is \[4-3i\] .
Final answer :
A conjugate of a complex number is nothing but the other complex number with the same real part and opposite imaginary part.

Note: The product of a complex number and its complex conjugate is a real number whose value is equal to the square of the magnitude of the complex number. We also need to know the value of the imaginary number \[i^{2}\] equals the minus of \[1\] . The value of the unit imaginary number \[i\] equals the square root of minus \[1\] . And the imaginary number \[i\] leads to another topic that is the complex plane .