# How do you divide (2-3i)(5i) /(2+3i)?

Oct 24, 2015

$\left(2 - 3 i\right) \left(\frac{5 i}{2 + 3 i}\right) = 60 - 25 i$

#### Explanation:

First step is to multiply $\left(2 - 3 i\right)$ by $5 i$:

$\left(2 - 3 i\right) \left(\frac{5 i}{2 + 3 i}\right) = \frac{10 i + 15}{2 + 3 i} = \frac{5 \left(3 + 2 i\right)}{2 + 3 i}$

Next step is to expand the fraction by complex conjugate of the denominator. In this way we get a real number in the denominator.

$\frac{5 \left(3 + 2 i\right)}{2 + 3 i} = \frac{5 \left(3 + 2 i\right) \left(2 - 3 i\right)}{\left(2 + 3 i\right) \left(2 - 3 i\right)} =$

$= \frac{5 \left(12 - 5 i\right)}{4 - 3} = 60 - 25 i$