Question

How do you find the conjugate of $5i-4$?

Answer 1

Hint: The given is the complex number and we have to find the conjugate for the given complex number. As we know that complex conjugate of any number is found by changing the sign of the imaginary part. By using this concept we get the desired answer.

Complete step by step solution:
We have been given $5i-4$.
We have to find the conjugate of the given complex number.
We know that a complex number is a number that can be represented in the form $a+ib$ where a and b are real numbers and $i$ is the imaginary number. To find the conjugate of the given number we need to change the sign of the middle term (imaginary part) by its opposite sign.
To write a complex number first we will write the real part and then the imaginary part. So we can write the given number as
$\Rightarrow -4+5i$
Now, the complex conjugate of the above obtained number will be
$\Rightarrow -4-5i$
Hence we get the conjugate of $5i-4$ as $-4-5i$.

Note: The fact is that the product of a complex number and its conjugate is always a real number. The possibility of mistake in finding the conjugate in this particular question is that students may change the sign of the middle term i.e. 4 and get the conjugate as $ 5i+4$ which is incorrect. So be careful as we need to change the sign of the imaginary part only.