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.

${\mathit{i}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathit{i}\mathbf{+}\mathbf{1}$

Short answer

Factorize the complex number.

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

The complex number is $0+2i$.

Step-by-step solution

Given Information

The complex number is$i^2+2i+1$ .

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.

$\begin{array}{rcl}i& =& \sqrt{-1}\\ i^2+2i+1& =& (\sqrt{-1}{)}^2+2i+1\\ & =& -1+2i+1\\ & =& 2i\\ & & \end{array}$

Hence, the complex number is $0+2i$ .

The graph is mentioned below.