# How do you multiply  (2+i)(2-3i)  in trigonometric form?

Oct 21, 2017

$7 - 4 i$

#### Explanation:

First, we have to know that
${i}^{1} = i$
${i}^{2} = - 1$
${i}^{3} = - i$
${i}^{4} = 1$

Then, we can expend the expression and simplify it with the above rule:

$\left(2 + i\right) \left(2 - 3 i\right)$
$= 4 - 6 i + 2 i - 3 {i}^{2}$
$= 4 - 4 i - 3 {i}^{2}$
$= 4 - 4 i - 3 \left(- 1\right)$
$= 4 - 4 i + 3$
$= 7 - 4 i$