Chapter 1: Q4P (page 1)

First simplify each of the following numbers to the $x + i y$ form or to the $r e^{i θ}$ form. Then plot the number in the complex plane.
$i^{2} + 2 i + 1$

Short Answer

Expert verified

Factorize the complex number.

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

The complex number is $0 + 2 i$ .

Step by step solution

Given Information

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

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.

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

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

The graph is mentioned below.

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First simplify each of the following numbers to the $x + i y$ form or to the $r e^{i θ}$ form. Then plot the number in the complex plane.
$i^{2} + 2 i + 1$

Short Answer

Step by step solution

Given Information

Definition of the Complex number

Find the value

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First simplify each of the following numbers to the x+iy form or to the reiθ form. Then plot the number in the complex plane.i2+2i+1

Short Answer

Step by step solution

Given Information

Definition of the Complex number

Find the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Force

Nuclear Physics

Electricity and Magnetism

Conservation of Energy and Momentum

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

First simplify each of the following numbers to the $x + i y$ form or to the $r e^{i θ}$ form. Then plot the number in the complex plane.
$i^{2} + 2 i + 1$