# How do you simplify i^43?

Jan 11, 2016

$- i$

#### Explanation:

We use the fact that ${i}^{2} = - 1$ to rewrite the expression and simplify :

${i}^{43} = {i}^{42} \cdot i$

$= {\left({i}^{2}\right)}^{21} \cdot i$

$= {\left(- 1\right)}^{21} \cdot i$

$= - i$