Question

Find the following quotient and express the answer in standard form of a complex number.

Answer 1

Hello, please consider the following.

When you have a complex number in the denominator you need to multiply by its conjugate to eliminate the imaginary component.

The conjugate of 4 - 3i is 4 + 3i, right?

So, let's do it!

$\dfrac{5-7i}{4-3i}=\dfrac{(5-7i)(4+3i)}{(4-3i)(4+3i)}\\\\=\dfrac{5(4+3i)-7i(4+3i)}{4^2-(3i)^2}\\\\=\dfrac{20+15i-28i-21i^2}{16+9}\\\\=\dfrac{20+21-13i}{25}\\\\\large \boxed{=\dfrac{41}{25}-\dfrac{13}{25}i\\}$

Thank  you.