Question

How do you find the conjugate of $12-4i$?

Answer 1

Hint: The given number is of the form $a+ib$ so the complex conjugate of the number is given by $a-ib$. So by simply changing the sign of the imaginary part of the given number we get the desired answer.

Complete step by step solution:
We have been given a complex number $12-4i$.
We have to find the conjugate of the given complex number.
Now, we know that a complex number is expressed as $a+ib$ where a and b are real numbers and $i$ is the imaginary part and the given number is of the standard form. Here 12 and 4 are real numbers and $i$ is the imaginary part.
Now, we know that the complex conjugate of the complex number is found by just changing the sign of its imaginary part by its opposite sign i.e. plus to minus or minus to plus and the sign of the real part remains the same.
Now, by changing the sign of the imaginary part of the given number we get the conjugate of the $12-4i$ as
$\Rightarrow 12+4i$
Hence above is the required complex conjugate of the given complex number.

Note: A complex number has both real and imaginary parts. The point to be remembered is that if the imaginary part of the complex number is zero then it is equal to its complex conjugate. Also the real part of the complex number does not change.