Question

Simplify 13 over the quantity of negative 3 plus 2i.

−3 + 2i
−3 − 2i
2i + 3
−2i + 3

Answer 1

`(13)/((-3+2i))`

To simplify we need to rationalize it. which can be done by multiplying composite of denominator. That is multiply by -3-2i

`=(13)/((-3+2i))*((-3-2i))/((-3-2i))`

Now multiply numerator with numerator and denominator with denominator

`=((-39-26i))/((-3)^2-(-2i)^2)`

`=((-39-26i))/(9-(4i^2))`

`=((-39-26i))/(9-(4(-1)))`

`=((-39-26i))/(9-(-4))`

`=((-39-26i))/(9+4)`

`=((-39-26i))/(13)`

`=-3-2i`

Hence final answer is
`=-3-2i`