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, Problem 45SGA
To determine

To express: the complex number in polar form.

Expert Solution & Answer
Check Mark

Answer to Problem 45SGA

  2(cos(2π3)+isin(2π3))

Explanation of Solution

Given information:

  1+3i

Calculation:

The coordinates (x,y) obtained from the complex number is (1,3) . Put the coordinates (x,y) in the formula given below and evaluate the value of  r .

  r=x2+y2=(1)2+(3)2=4=2

Put the coordinates (x,y) in the formula given below and evaluate  θ .

  θ=arctan(yx)+π                                          [x<0]=arctan(31)+π=π3+π=2π3

The polar form can be evaluated as shown below.

  Polar form=r(cosθ+isinθ)=2(cos(2π3)+isin(2π3))                                      [Put r and θ]

Thus the polar form of the given complex number is 2(cos(2π3)+isin(2π3)) .

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 - Prob. 2CFUCh. 9.4 - Prob. 3CFUCh. 9.4 - Prob. 4CFUCh. 9.4 - Prob. 5CFUCh. 9.4 - Prob. 6CFUCh. 9.4 - Prob. 7CFUCh. 9.4 - Prob. 8CFUCh. 9.4 - Prob. 9CFUCh. 9.4 - Prob. 10CFUCh. 9.4 - Prob. 11CFUCh. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - Prob. 23ECh. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.4 - Prob. 26ECh. 9.4 - Prob. 27ECh. 9.4 - Prob. 28ECh. 9.4 - Prob. 29ECh. 9.4 - Prob. 30ECh. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.4 - Prob. 39ECh. 9.4 - Prob. 40ECh. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.4 - Prob. 43ECh. 9.4 - Prob. 44ECh. 9.4 - Prob. 1MCQCh. 9.4 - Prob. 2MCQCh. 9.4 - Prob. 3MCQCh. 9.4 - Prob. 4MCQCh. 9.4 - Prob. 5MCQCh. 9.4 - Prob. 6MCQCh. 9.4 - Prob. 7MCQCh. 9.4 - Prob. 8MCQCh. 9.4 - Prob. 9MCQCh. 9.4 - 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 - Prob. 50SGACh. 9 - Prob. 51SGACh. 9 - Prob. 52SGACh. 9 - Prob. 53SGACh. 9 - Prob. 54SGACh. 9 - Prob. 55SGACh. 9 - Prob. 56SGACh. 9 - Prob. 57SGACh. 9 - Prob. 58SGACh. 9 - Prob. 59SGACh. 9 - Prob. 60SGACh. 9 - Prob. 61SGACh. 9 - Prob. 62SGACh. 9 - Prob. 63SGACh. 9 - Prob. 64SGACh. 9 - Prob. 65SGACh. 9 - Prob. 66SGACh. 9 - Prob. 67SGACh. 9 - Prob. 68SGACh. 9 - Prob. 1SAPCh. 9 - Prob. 2SAPCh. 9 - Prob. 3SAPCh. 9 - Prob. 4SAPCh. 9 - Prob. 5SAPCh. 9 - Prob. 6SAPCh. 9 - Prob. 7SAPCh. 9 - Prob. 8SAPCh. 9 - Prob. 9SAPCh. 9 - Prob. 10SAP
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Write the Complex Number in Trigonometric (Polar) Form; Author: The Math Sorcerer;https://www.youtube.com/watch?v=9kZOHHRjfIQ;License: Standard YouTube License, CC-BY