Question

Simplify the given expression:

4 divided by the quantity of 3 minus 2i

Answer 1

Multiply by the `conjugate` of the denominator,
\[\Large\rm \frac{4}{3-2\mathcal i}\color{royalblue}{\left(\frac{3+2\mathcal i}{3+2\mathcal i}\right)}\]

Answer 2

multiplying complex conjugates gives us the `sum of their squares`,
\[\Large\rm (a-\mathcal i b)(a+\mathcal i b)=a^2+b^2\]So that's what happening in the denominator,\[\Large\rm \frac{4(3+2\mathcal i)}{3^2+2^2}\]

Answer 3

Just requires a little bit of work to simplify it from there.