Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set - Page 570: 107

Answer

$1-i$.

Work Step by Step

The given expression is $=\frac{i^4+i^{12}}{i^8-i^7}$ Factor each term. $=\frac{(i^2)^2+(i^{2})^6}{(i^2)^4-(i^2)^3i}$ Use $i^2=-1$ $=\frac{(-1)^2+(-1)^6}{(-1)^4-(-1)^3i}$ Simplify. $=\frac{1+1}{1+i}$ $=\frac{2}{1+i}$ The conjugate of the denominator is $1-i$. Multiply the numerator and the denominator by $1-i$. $=\frac{2}{1+i}\cdot \frac{1-i}{1-i}$ Use the special formula $(A+B)^2=A^2+2AB+B^2$ $=\frac{2(1-i)}{1^2-i^2}$ Use $i^2=-1$. $=\frac{2(1-i)}{1+1}$ Simplify. $=\frac{2(1-i)}{2}$ $=1-i$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.