Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Review Exercises - Page 409: 15



Work Step by Step

Step 1: Multiplying both the numerator and the denominator by the complex conjugate of the denominator: $\frac{25-19i}{5+3i}\times\frac{5-3i}{5-3i}$ Step 2: $\frac{(25-19i)(5-3i)}{(5+3i)(5-3i)}=\frac{25(5-3i)-19i(5-3i)}{(5)^{2}-(3i)^{2}}=\frac{125-75i-95i+57i^{2}}{25-9i^{2}}$ Step 3: $\frac{125-75i-95i+57i^{2}}{25-9i^{2}}=\frac{125-170i-57}{25+9}=\frac{68-170i}{34}$ Step 4: $\frac{68-170i}{34}=\frac{34(2-5i)}{34}=2-5i$
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