Question

How do you simplify$i^{(-999)}$?

Answer 1

Solve for the required value.

The value of $i$is $\sqrt{-1}.$

$$\begin{gathered} i=\sqrt{-1} \\ {i}^2=-1 \end{gathered}$$

Now,

$i^{(-999)}$

$$\begin{gathered} ={\left(i^2\right)}^{-499}\times i^{-1} \\ ={(-1)}^{-499}\times \frac{1}{i} \\ =-\frac{1}{i} \\ =i \end{gathered}$$

Hence, the required value of $i^{(-999)}$ is $i.$