/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 100 Explain how to find the power of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 100

Explain how to find the power of a complex number in polar form.

Short Answer

Expert verified
To find the power 'n' of a complex number in polar form \(z = r (\cos 胃 + i \sin 胃)\), use the formula \(z^n = r^n (\cos(n胃) + i \sin(n胃))\), where \(r^n\) is the magnitude and n胃 is the angular argument of the resultant complex number.

Step by step solution

01

Identify the values of r, 胃 and n

Given a complex number in polar form, \(z = r (\cos 胃 + i \sin 胃)\), and that it needs to be raised to the power of 'n', identify the values of r (magnitude), 胃 (angle in radians) and 'n' (power). Remember r > 0, 0 鈮� 胃 < 2蟺 and n is an integer.
02

Use the power of complex number formula

Having identified the values of r, 胃, and n, use the formula to find the power of the complex number in polar form, which is \(z^n = r^n (\cos(n胃) + i \sin(n胃))\). Here 'r' raised to the power 'n' represents the magnitude of the resultant complex number, and arguments of the resultant complex numbers are given by n胃.
03

Simplify to find z^n

Simplify the right side of the equation to find the expression for z^n, the power of the complex number in polar form.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Graph the spiral \(r=\frac{1}{\theta} .\) Use a \([-1.6,1.6,1]\) by \([-1,1,1]\) viewing rectangle. Let \(\theta \min =0\) and \(\theta \max =2 \pi,\) then \(\theta \min =0\) and \(\theta \max =4 \pi,\) and finally \(\theta \min =0\) and \(\theta \max =8 \pi\)

You want to fly your small plane due north, but there is a 75-kilometer wind blowing from west to east. a. Find the direction angle for where you should head the plane if your speed relative to the ground is 310 kilometers per hour. b. If you increase your airspeed, should the direction angle in part (a) increase or decrease? Explain your answer.

Use a sketch to find the exact value of \(\cos \left(\tan ^{-1} \frac{3}{4}\right)\)

Explaining the Concepts Describe the test for symmetry with respect to the line \(\theta=\frac{\pi}{2}\)

In Exercises \(81-86,\) solve equation in the complex number system. Express solutions in polar and rectangular form. $$ x^{6}+1=0 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.