Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 8 - Application of Trigonometry - 8.5 Trigonometric (Polar) Form of Complex Numbers: Products and Quotients - 8.5 Exercises - Page 802: 95

Answer

$$0.6537 + 7.4715i$$

Work Step by Step

$$\eqalign{ & \left[ {2.5\left( {\cos 35^\circ + i\sin 35^\circ } \right)} \right]\left[ {3.0\left( {\cos 50^\circ + i\sin 50^\circ } \right)} \right] \cr & {\text{Multiply use the product theorem}} \cr & = \left( {2.5 \times 3.0} \right)\left[ {\cos \left( {35^\circ + 50^\circ } \right) + i\sin \left( {35^\circ + 50^\circ } \right)} \right] \cr & = 7.5\left[ {\cos 85^\circ + i\sin 85^\circ } \right] \cr & {\text{Use a calculator}} \cr & \approx 0.6537 + 7.4715i \cr} $$
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