Question

How do you write the complex conjugate of the complex number $5-4i$?

Answer 1

We are given a complex number $5-4i$ in the standard form. And we have to re- write the given expression as the complex conjugate of the complex number. Complex conjugate means that the sign of the imaginary part in the complex number will be switched to the opposite one, that is, $x+iy$ is the complex number then the complex conjugate will have the imaginary part with its sign switched, so we will get $x-iy$.

Complete step by step answer:
According to the given question, we are given a complex number which is already in the standard form. Now, we are asked to write the complex conjugate of the complex number.
Let us see, what complex conjugate stands for.
Complex conjugate refers to the switching of the sign of the imaginary part in a complex number to the opposite one.
Suppose we have a complex number $x+iy$ and we are supposed to write the complex conjugate.
Then, as per stated above, the complex conjugate of the complex number $x+iy$ is $x-iy$.
For example – we have a complex number $\sqrt{3}+i5\sqrt{3}$, the complex conjugate of the given complex number will be $\sqrt{3}-i5\sqrt{3}$.
The given complex number that we have is,
$5-4i$----(1)
Now, we have to find the complex conjugate of the same. As discussed above, we only switch the sign of the imaginary part. So, we have,
$5+4i$

Therefore, the complex conjugate of the given complex number is $5+4i$.

Note: While dealing with complex conjugate, we only switch the sign of the imaginary part. The sign of the real part in the complex number should not be switched but is kept as it is. The possible mistakes that can be done are writing the conjugate as -5-4i or -5+4i. So, students must be aware of sign change to be done for which term.