Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 8 - Section 8.3 - Products and Quotients in Trigonometric Form - 8.3 Problem Set - Page 439: 6

Answer

$12[cos50^{\circ}+isin50^{\circ}]$

Work Step by Step

$if\\ $ $z_1=r_1(cosθ_1+isinθ_1)\\$ $and\\$ $z_2=r_2(cosθ_2+isinθ_2)\\$ $then\\$ $z_1z_2=r_1r_2[cos(θ_1+θ_2)+isin(θ_1+θ_2)]$ $given\ problem\\$ $3(cos 20° +i sin 20°) 4(cos 30° + i sin 30°)\\$ $here\ r1=3,r2=4,θ1=20,θ2=30\\$ $=3∗4[cos(20^{\circ}+30^{\circ})+isin(20^{\circ}+30^{\circ})\\$ $=12[cos50^{\circ}+isin50^{\circ}]$
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