Question

First simplify each of the following numbers to the $\mathit{x}\mathbf{+}\mathit{i}\mathit{y}$form or to the $\mathit{r}{\mathit{e}}^{\mathbf{i}\mathbf{\theta }}$form. Then plot the number in the complex plane.

${\mathit{i}}^{\mathbf{4}}$

.

Short answer

The complex number is $1+0i$.

Step-by-step solution

Given Information

The complex number is$i^4$ .

Definition of the Complex number

A complex number is a number that is made up of both real and imaginary numbers

Find the value

Factorize the complex number.

$\begin{array}{rcl}i& =& \sqrt{-1}\\ i^4& =& (\sqrt[2]{-1}{)}^4\\ & =& (-1{)}^{\frac{4}{2}}\\ & =& 1\\ & & \end{array}$

Hence, the complex number is $1+0i$ .

The graph is mentioned below.