Chapter 1: Q2P (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.
$\frac{1}{1 - i}$ .
.

Short Answer

Expert verified

Rationalize the complex number.

$\begin{array}{rcl} \frac{1}{i - 1} & = & \frac{1}{i - 1} \cdot \frac{i + 1}{i + 1} \\ = & \frac{i + 1}{i^{2} - i^{2}} \\ = & \frac{i + 1}{- 2} \\ = & - \frac{1}{2} - \frac{i}{2} \end{array}$

The complex number is $- \frac{1}{2} - \frac{i}{2}$ .

Step by step solution

Given Information

The complex number is $\frac{1}{1 - i}$ .

Definition of the Complex number

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

Find the value

Rationalize the complex number.

$\begin{array}{rcl} \frac{1}{i - 1} & = & \frac{1}{i - 1} \cdot \frac{i + 1}{i + 1} \\ = & \frac{i + 1}{i^{2} - i^{2}} \\ = & \frac{i + 1}{- 2} \\ = & - \frac{1}{2} - \frac{i}{2} \end{array}$

Hence, the complex number is $- \frac{1}{2} - \frac{i}{2}$ .

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.
$\frac{1}{1 - i}$ .
.

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 reiθform. Then plot the number in the complex plane.11-i..

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

Circular Motion and Gravitation

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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.
$\frac{1}{1 - i}$ .
.