# How do you find the power (3-6i)^4 and express the result in rectangular form?

Dec 22, 2016

${\left(3 - 6 i\right)}^{4} = - 567 + 1944 i$

#### Explanation:

I would just square twice in rectangular form:

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

$\textcolor{w h i t e}{{\left(3 - 6 i\right)}^{2}} = {3}^{2} {\left(1 - 2 i\right)}^{2}$

$\textcolor{w h i t e}{{\left(3 - 6 i\right)}^{2}} = 9 \left(1 - 4 i - 4\right)$

$\textcolor{w h i t e}{{\left(3 - 6 i\right)}^{2}} = 9 \left(- 3 - 4 i\right)$

$\textcolor{w h i t e}{}$

${\left(9 \left(- 3 - 4 i\right)\right)}^{2} = {9}^{2} {\left(3 + 4 i\right)}^{2}$

$\textcolor{w h i t e}{{\left(9 \left(- 3 - 4 i\right)\right)}^{2}} = 81 \left(9 + 24 i - 16\right)$

$\textcolor{w h i t e}{{\left(9 \left(- 3 - 4 i\right)\right)}^{2}} = 81 \left(- 7 + 24 i\right)$

$\textcolor{w h i t e}{{\left(9 \left(- 3 - 4 i\right)\right)}^{2}} = - 567 + 1944 i$