# How do you simplify (-7+4i)^2+(12+12i)+(2i)+(5i)?

Oct 6, 2016

You separate the real and imaginary components.

#### Explanation:

${\left(- 7 + 4 i\right)}^{2} = \left(- 7 + 4 i\right) \left(- 7 + 4 i\right)$ $=$ $49 - 56 i + 16 {i}^{2}$

$=$ $33 - 56 i$, as $16 {i}^{2}$ $=$ $- 16$.

And simply add the residue $12 + 19 i$, to give:

$33 - 56 i + 12 + 19 i$ $=$ ???