Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 1 - 1.5 - Complex Numbers - 1.5 Exercises - Page 120: 92

Answer

False. $i^{44}+i^{150}-i^{74}-i^{109}+i^{61}=1$

Work Step by Step

$i^{44}+i^{150}-i^{74}-i^{109}+i^{61}=(i^2)^{22}+(i^2)^{75}-(i^2)^{37}-i(i^{108})+i(i^{60})=(-1)^{22}+(-1)^{75}-(-1)^{37}-i(i^2)^{54}+i(i^2)^{30}=1-1-(-1)-i(-1)^{54}+i(-1)^{30}=1-i+i=1$
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