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

Feb 16, 2016

${\left(2 + 3 i\right)}^{2} = 12 i - 5$

#### Explanation:

You should know that ${i}^{2} = - 1$. Then,

${\left(2 + 3 i\right)}^{2} = {\left(2\right)}^{2} + 2 \left(3 i\right) \left(2\right) + {\left(3 i\right)}^{2}$

$= 4 + 12 i + 9 {i}^{2}$

$= 4 + 12 i - 9$

$= 12 i - 5$