Question

if i equals the square root of -1, what is the value of i to the power of 3

Answer 1

We know that

$i=\sqrt{-1}$

Then, we elevate each side to the third power

$i^3=(\sqrt{-1})^3$

We have to use the following power property

$(\sqrt{a})^b=\sqrt{a^b}$

So, we have

$\begin{gathered} i^3=\sqrt{(-1)^3} \\ i^3=\sqrt{-1} \end{gathered}$

Since the cubic power of -1 is actually -1.

Therefore, the answer is

$i^3=\sqrt{-1}$