Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.1 Complex Numbers - 8.1 Exercises - Page 358: 82

Answer

$4-i$

Work Step by Step

Step 1: Multiplying the expression by the complex conjugate of the denominator in both the numerator and the denominator: $\frac{14+5i}{3+2i}\times\frac{3-2i}{3-2i}$ Step 2: $\frac{14+5i}{3+2i}\times\frac{3-2i}{3-2i}=\frac{(14+5i)(3-2i)}{(3)^{2}-(2i)^{2}}$ Step 3: $\frac{(14+5i)(3-2i)}{(3)^{2}-(2i)^{2}}=\frac{42-28i+15i-10i^{2}}{9-4i^{2}}=\frac{42-13i-10(-1)}{9-4(-1)}$ Step 4: $\frac{42-13i-10(-1)}{9-4(-1)}=\frac{42-13i+10}{13}=\frac{52-13i}{13}$ Step 5: $\frac{52-13i}{13}=\frac{13(4-i)}{13}=4-i$
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