Question

How do you write the complex conjugate of the complex number $84 - 63i$

Answer 1

As first of all we have to understand about the following term:
Complex number: It is the number that is expressed in the form of $a + ib$ where, $a,b$ are real numbers and $'i'$ is an imaginary number called “iota”.
The value of $i = \sqrt { - 1}$ .
For example $z = a + ib$ is a complex number.

Complete step by step solution:
To solve it first understand what the complex conjugate of a complex number is: the number which have equal real and imaginary parts but they are opposite in sign.
For example, $z = a + ib$ then its complex conjugate will be $\bar z = a - ib$ .
So, as given in question $z = 84 - 63i$
Then as mentioned above the complex conjugate of a complex number will obtain by just changing the sign.
So, $\bar z = 84 + 63i$
The complex conjugate of the complex number $z = 84 - 63i$ is $\bar z = 84 + 63i$ .

Note: A complex number is equal to its complex conjugate if its imaginary part is zero, or the number is real. So, we can say real numbers are the only fixed point of conjugation. Conjugation is an involution that means the conjugate of the complex conjugate of a complex number $z$ will be $z$ .