Question

How do you divide `(-2+3i)/(3-2i)`?

Answer 1

The answer is `-12/13+(5i)/13`

Explanation:

To simplify, multiply numerator and denominatorby the conjugate of the denominator
if `z=a+ib` the the conjugate is `barz=a-ib`
so the conjugate of the denominator is `3+2i`
and `i^2=-1`
Then the expression is `(-2+3i)/(3-21)=((-2+3i)(3+2i))/((3-2i)(3+2i))`

`=(-6-4i+9i+6i^2)/(9-4i^2)=(-12+5i)/(13)=-12/13+(5i)/13`