Question

The conjugate of $z = 3 + 4i$ is:
A.The reflection in the x-axis
B.The reflection in the y-axis
C.The reflection in the origin
D.The reflection of (-3+4i) in the real axis

Answer 1

Hint : In this question, we need to determine the complex conjugate of the given complex number and comment on its reflection image. For this, we will follow the properties of the complex numbers along with the use of the coordinate axes.

Complete step-by-step answer :
Complex numbers are the summation of the real as well as the imaginary part of the numbers. Complex numbers are defined on the coordinate axes such that the real part lies towards the x-axis and the imaginary part lies towards the y-axis.
To differentiate the real and the imaginary part, a term ‘i’ or ‘j’ known as ‘iota’ is associated with the imaginary part of the complex number. The mathematical value of the term ‘i' or ‘j’ is $\sqrt { - 1}$ .
The conjugate of the complex number is the conversion of the complex part of the complex numbers to the negation of the initial part such as the complex conjugate of the complex number $a + ib$ is given as $a - ib$ .
So, the complex conjugate of $z = 3 + 4i$ is given as $\bar z = 3 - 4i$ .
In other words, we can say that the complex conjugate is the mirror reflection of the complex numbers along the x-axis as we only convert the imaginary part and not the real part of the complex numbers.

So, the correct answer is “Option A”.

Note : The reflection along the y-axis will convert the real part of the complex number while keeping the imaginary part constant. Reflection in the origin converts the real as well as the imaginary part of the complex numbers. The reflection of (-3+4i) in the real axis will give (-3-4i).