# How do you divide (3+10i)^2?

Sep 25, 2017

$- 91 + 60 i$

#### Explanation:

There is no division involved in this problem.

However,

${\left(3 + 10 i\right)}^{2} = \left(3 + 10 i\right) \left(3 + 10 i\right)$
$\text{ } = \left(3\right) \left(3\right) + \left(3\right) \left(10 i\right) + \left(3\right) \left(10 i\right) + \left(10 i\right) \left(10 i\right)$
$\text{ } = 9 + 60 i + 100 {i}^{2}$
$\text{ } = 9 + 60 i - 100 \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \left(\because {i}^{2} = - 1\right)$
$\text{ } = - 91 + 60 i$