# How do you simplify 3i^2 - 4i^4 + 5i^8 + 3 and write in a+bi form?

Nov 27, 2015

Remember $\textcolor{red}{{i}^{2} = - 1}$ ; $\textcolor{b l u e}{{i}^{4} = 1}$

$3 {i}^{2} - 4 {i}^{4} + 5 {i}^{8} + 3$

Can be rewrite as
$3 {i}^{2} - 4 {i}^{4} _ 5 {\left({i}^{4}\right)}^{2} + 3$
$\implies = 3 \cdot \textcolor{red}{- 1} - 4 \cdot \left(\textcolor{b l u e}{1}\right) + 5 \cdot {\textcolor{b l u e}{1}}^{2} + 3$
$\implies = - 3 - 4 + 5 + 3$
$\implies = 1$

In $a \pm b i$ form
$1 \pm 0 i$