Simplify the given expression below: 4 divided by the quantity of 3 minus 2i

This is rationalising the denominator of an imaginary fraction. We want to remove all i's from the denominator.

To do this, we multiply the fraction by 1. However 1 can be expressed in an infinite number of ways. For example, 1 = 2/2 = 3/3 = 4n^2 / 4n^2 (assuming n is not zero!). Let's express 1 as the complex conjugate of the denominator, divided by the complex conjugate of the denominator.

The complex conjugate of (3 - 2i) is (3 + 2i). Then do what I just said:

4/(3-2i) * (3+2i)/(3+2i) = 4(3+2i)/(3-2i)(3+2i) = (12+8i)/(9-4i^2) = (12+8i)/(9+4) = (12+8i)/13

This is the answer you are looking for. I hope this helps :)