How do you simplify 1/i^3?

Sep 18, 2016

$i$

Explanation:

The first step is to evaluate ${i}^{3}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{i}^{2} = {\left(\sqrt{- 1}\right)}^{2} = - 1} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow {i}^{3} = {i}^{2.} i = - i$

Thus $\frac{1}{i} ^ 3 = \frac{1}{- i}$

multiply numerator/denominator by i.

$\Rightarrow \frac{1}{- i} \times \frac{i}{i} = \frac{i}{- {i}^{2}} = i$