Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Chapter 9.8, Problem 30E
To determine

To solve the given equation and then graph the roots in the complex plane.

Expert Solution & Answer
Check Mark

Answer to Problem 30E

  x1=28[cos(π16)+isin(π16)]x2=28[cos(9π16)+isin(9π16)]x3=28[cos(17π16)+isin(17π16)]x4=28[cos(25π16)+isin(25π16)]

Explanation of Solution

Given:

The given equation is x4(1+i)=0

Calculation:

Simplifying the given equation

  x4(1+i)=0x4=(1+i)x=(1+i)14

Writing the complex number in polar form

  x=[2(cosπ4+isinπ4)]14

Now find the roots as follows

  x=28[cos(π16)+isin(π16)]

So, the roots are-

  x1=28[cos(π16)+isin(π16)]x2=28[cos(9π16)+isin(9π16)]x3=28[cos(17π16)+isin(17π16)]x4=28[cos(25π16)+isin(25π16)]

The following is the graph of the solutions-

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 9.8, Problem 30E

Chapter 9 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 9.1 - Prob. 11CFUCh. 9.1 - Prob. 12CFUCh. 9.1 - Prob. 13CFUCh. 9.1 - Prob. 14CFUCh. 9.1 - Prob. 15CFUCh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - Prob. 56ECh. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - Prob. 59ECh. 9.1 - Prob. 60ECh. 9.1 - Prob. 61ECh. 9.1 - Prob. 62ECh. 9.1 - Prob. 63ECh. 9.1 - Prob. 64ECh. 9.1 - Prob. 65ECh. 9.2 - Prob. 1CFUCh. 9.2 - Prob. 2CFUCh. 9.2 - Prob. 3CFUCh. 9.2 - Prob. 4CFUCh. 9.2 - Prob. 5CFUCh. 9.2 - Prob. 6CFUCh. 9.2 - Prob. 7CFUCh. 9.2 - Prob. 8CFUCh. 9.2 - Prob. 9CFUCh. 9.2 - Prob. 10CFUCh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.3 - Prob. 1CFUCh. 9.3 - Prob. 2CFUCh. 9.3 - Prob. 3CFUCh. 9.3 - Prob. 4CFUCh. 9.3 - Prob. 5CFUCh. 9.3 - Prob. 6CFUCh. 9.3 - Prob. 7CFUCh. 9.3 - Prob. 8CFUCh. 9.3 - Prob. 9CFUCh. 9.3 - Prob. 10CFUCh. 9.3 - Prob. 11CFUCh. 9.3 - Prob. 12CFUCh. 9.3 - Prob. 13CFUCh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - Prob. 34ECh. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.3 - Prob. 39ECh. 9.3 - Prob. 40ECh. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - Prob. 44ECh. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48ECh. 9.3 - Prob. 49ECh. 9.3 - Prob. 50ECh. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Prob. 53ECh. 9.3 - Prob. 54ECh. 9.3 - Prob. 55ECh. 9.4 - Prob. 1CFUCh. 9.4 - 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Prob. 10MCQCh. 9.5 - Prob. 1CFUCh. 9.5 - Prob. 2CFUCh. 9.5 - Prob. 3CFUCh. 9.5 - Prob. 4CFUCh. 9.5 - Prob. 5CFUCh. 9.5 - Prob. 6CFUCh. 9.5 - Prob. 7CFUCh. 9.5 - Prob. 8CFUCh. 9.5 - Prob. 9CFUCh. 9.5 - Prob. 10CFUCh. 9.5 - Prob. 11CFUCh. 9.5 - Prob. 12CFUCh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.5 - Prob. 36ECh. 9.5 - Prob. 37ECh. 9.5 - Prob. 38ECh. 9.5 - Prob. 39ECh. 9.5 - Prob. 40ECh. 9.5 - Prob. 41ECh. 9.5 - Prob. 42ECh. 9.5 - Prob. 43ECh. 9.5 - Prob. 44ECh. 9.5 - Prob. 45ECh. 9.5 - Prob. 46ECh. 9.5 - Prob. 47ECh. 9.5 - Prob. 48ECh. 9.5 - Prob. 49ECh. 9.5 - Prob. 50ECh. 9.5 - Prob. 51ECh. 9.5 - Prob. 52ECh. 9.5 - Prob. 53ECh. 9.5 - Prob. 54ECh. 9.5 - Prob. 55ECh. 9.6 - Prob. 1CFUCh. 9.6 - Prob. 2CFUCh. 9.6 - Prob. 3CFUCh. 9.6 - Prob. 4CFUCh. 9.6 - Prob. 5CFUCh. 9.6 - Prob. 6CFUCh. 9.6 - Prob. 7CFUCh. 9.6 - Prob. 8CFUCh. 9.6 - Prob. 9CFUCh. 9.6 - Prob. 10CFUCh. 9.6 - Prob. 11CFUCh. 9.6 - Prob. 12CFUCh. 9.6 - Prob. 13CFUCh. 9.6 - Prob. 14CFUCh. 9.6 - Prob. 15CFUCh. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - Prob. 18ECh. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Prob. 21ECh. 9.6 - Prob. 22ECh. 9.6 - Prob. 23ECh. 9.6 - Prob. 24ECh. 9.6 - Prob. 25ECh. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Prob. 28ECh. 9.6 - Prob. 29ECh. 9.6 - Prob. 30ECh. 9.6 - Prob. 31ECh. 9.6 - Prob. 32ECh. 9.6 - Prob. 33ECh. 9.6 - Prob. 34ECh. 9.6 - Prob. 35ECh. 9.6 - Prob. 36ECh. 9.6 - Prob. 37ECh. 9.6 - Prob. 38ECh. 9.6 - Prob. 39ECh. 9.6 - Prob. 40ECh. 9.6 - Prob. 41ECh. 9.6 - Prob. 42ECh. 9.6 - Prob. 43ECh. 9.6 - Prob. 44ECh. 9.6 - Prob. 45ECh. 9.6 - Prob. 46ECh. 9.6 - Prob. 47ECh. 9.6 - Prob. 48ECh. 9.6 - Prob. 49ECh. 9.6 - Prob. 50ECh. 9.6 - Prob. 51ECh. 9.6 - Prob. 52ECh. 9.6 - Prob. 53ECh. 9.6 - Prob. 54ECh. 9.6 - Prob. 55ECh. 9.6 - Prob. 56ECh. 9.6 - Prob. 57ECh. 9.6 - Prob. 58ECh. 9.6 - Prob. 59ECh. 9.6B - Prob. 1GCECh. 9.6B - Prob. 2GCECh. 9.6B - Prob. 3GCECh. 9.6B - Prob. 4GCECh. 9.6B - Prob. 5GCECh. 9.6B - Prob. 6GCECh. 9.6B - Prob. 7GCECh. 9.6B - Prob. 8GCECh. 9.7 - Prob. 1CFUCh. 9.7 - Prob. 2CFUCh. 9.7 - Prob. 3CFUCh. 9.7 - Prob. 4CFUCh. 9.7 - Prob. 5CFUCh. 9.7 - Prob. 6CFUCh. 9.7 - Prob. 7CFUCh. 9.7 - Prob. 8CFUCh. 9.7 - Prob. 9CFUCh. 9.7 - Prob. 10ECh. 9.7 - Prob. 11ECh. 9.7 - Prob. 12ECh. 9.7 - Prob. 13ECh. 9.7 - Prob. 14ECh. 9.7 - Prob. 15ECh. 9.7 - Prob. 16ECh. 9.7 - Prob. 17ECh. 9.7 - Prob. 18ECh. 9.7 - Prob. 19ECh. 9.7 - Prob. 20ECh. 9.7 - Prob. 21ECh. 9.7 - Prob. 22ECh. 9.7 - Prob. 23ECh. 9.7 - Prob. 24ECh. 9.7 - Prob. 25ECh. 9.7 - Prob. 26ECh. 9.7 - Prob. 27ECh. 9.7 - Prob. 28ECh. 9.7 - Prob. 29ECh. 9.7 - Prob. 30ECh. 9.7 - Prob. 31ECh. 9.7 - Prob. 32ECh. 9.7 - Prob. 33ECh. 9.7 - Prob. 34ECh. 9.7 - Prob. 35ECh. 9.7 - Prob. 36ECh. 9.7 - Prob. 37ECh. 9.7 - Prob. 38ECh. 9.7 - Prob. 1GCECh. 9.7 - Prob. 2GCECh. 9.7 - Prob. 3GCECh. 9.7 - Prob. 4GCECh. 9.7 - Prob. 5GCECh. 9.7 - Prob. 6GCECh. 9.8 - Prob. 1CFUCh. 9.8 - Prob. 2CFUCh. 9.8 - Prob. 3CFUCh. 9.8 - Prob. 4CFUCh. 9.8 - Prob. 5CFUCh. 9.8 - Prob. 6CFUCh. 9.8 - Prob. 7CFUCh. 9.8 - Prob. 8CFUCh. 9.8 - Prob. 9CFUCh. 9.8 - Prob. 10CFUCh. 9.8 - Prob. 11CFUCh. 9.8 - Prob. 12ECh. 9.8 - Prob. 13ECh. 9.8 - Prob. 14ECh. 9.8 - Prob. 15ECh. 9.8 - Prob. 16ECh. 9.8 - Prob. 17ECh. 9.8 - Prob. 18ECh. 9.8 - Prob. 19ECh. 9.8 - Prob. 20ECh. 9.8 - Prob. 21ECh. 9.8 - Prob. 22ECh. 9.8 - Prob. 23ECh. 9.8 - Prob. 24ECh. 9.8 - Prob. 25ECh. 9.8 - Prob. 26ECh. 9.8 - Prob. 27ECh. 9.8 - Prob. 28ECh. 9.8 - Prob. 29ECh. 9.8 - Prob. 30ECh. 9.8 - Prob. 31ECh. 9.8 - Prob. 32ECh. 9.8 - Prob. 33ECh. 9.8 - Prob. 34ECh. 9.8 - Prob. 35ECh. 9.8 - Prob. 36ECh. 9.8 - Prob. 37ECh. 9.8 - Prob. 38ECh. 9.8 - Prob. 39ECh. 9.8 - Prob. 40ECh. 9.8 - Prob. 41ECh. 9.8 - Prob. 42ECh. 9.8 - Prob. 43ECh. 9.8 - Prob. 44ECh. 9.8 - Prob. 45ECh. 9.8 - Prob. 46ECh. 9 - Prob. 1SGACh. 9 - Prob. 2SGACh. 9 - Prob. 3SGACh. 9 - Prob. 4SGACh. 9 - Prob. 5SGACh. 9 - Prob. 6SGACh. 9 - Prob. 7SGACh. 9 - Prob. 8SGACh. 9 - Prob. 9SGACh. 9 - Prob. 10SGACh. 9 - Prob. 11SGACh. 9 - Prob. 12SGACh. 9 - Prob. 13SGACh. 9 - Prob. 14SGACh. 9 - Prob. 15SGACh. 9 - Prob. 16SGACh. 9 - Prob. 17SGACh. 9 - Prob. 18SGACh. 9 - Prob. 19SGACh. 9 - Prob. 20SGACh. 9 - Prob. 21SGACh. 9 - Prob. 22SGACh. 9 - Prob. 23SGACh. 9 - Prob. 24SGACh. 9 - Prob. 25SGACh. 9 - Prob. 26SGACh. 9 - Prob. 27SGACh. 9 - Prob. 28SGACh. 9 - Prob. 29SGACh. 9 - Prob. 30SGACh. 9 - Prob. 31SGACh. 9 - Prob. 32SGACh. 9 - Prob. 33SGACh. 9 - Prob. 34SGACh. 9 - Prob. 35SGACh. 9 - Prob. 36SGACh. 9 - Prob. 37SGACh. 9 - Prob. 38SGACh. 9 - Prob. 39SGACh. 9 - Prob. 40SGACh. 9 - Prob. 41SGACh. 9 - Prob. 42SGACh. 9 - Prob. 43SGACh. 9 - Prob. 44SGACh. 9 - Prob. 45SGACh. 9 - Prob. 46SGACh. 9 - Prob. 47SGACh. 9 - Prob. 48SGACh. 9 - Prob. 49SGACh. 9 - 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