Algebra and Trigonometry 10th Edition

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

Chapter 1 - Review Exercises - Page 153: 76



Work Step by Step

Using the rules of imaginary numbers: $\frac{1}{2+i} = \frac{2-i}{2-i}=\frac{2-i}{2^2-i^2}=\frac{2-i}{5}$ $\frac{5}{1+4i} = \frac{5}{1+4i}*\frac{1-4i}{1-4i}=\frac{5-20i}{1-16i^2}=\frac{5-20i}{17}$ Write the final expression: $\frac{2-i}{5}-\frac{5-20i}{17} = \frac{17(2-i)+5(5-20i)}{17*5} = $$\frac{9+83i}{85}$
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