Question

nothing

Answer 1

do you know what the \(\bf conjugate\) of the denominator is?

Answer 2

conjugate of a binomial, is the same binomial, with a different sign

cat + dog, conjugate => cat - dog
cheese - bologne conjugate => cheese + bologne

Answer 3

so the idea behiind the simplification is to "rationalize" the denominator, or getting rid of the pesky "i" there

so that's done by using the conjuate like \(\bf \cfrac{4}{3-2i}\times \cfrac{3+2i}{3+2i}\implies \cfrac{4(3+2i)}{(3-2i)(3+2i)}\\ \quad \\
\textit{recall that }\qquad (a-b)(a+b) = a^2-b^2\qquad thus\\ \quad \\
\cfrac{4(3+2i)}{(3-2i)(3+2i)}\implies \cfrac{4(3+2i)}{3^2-(2i)^2}\)

so what does that give you in the denominator?

Answer 4

:)

Answer 5

yes you're correct, yw