Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.7 - Complex Numbers - Exercise Set: 67

Answer

$\dfrac{2}{3+i}=\dfrac{3}{5}-\dfrac{1}{5}i$

Work Step by Step

$\dfrac{2}{3+i}$ Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator: $\dfrac{2}{3+i}=\dfrac{2}{3+i}\cdot\dfrac{3-i}{3-i}=\dfrac{2(3-i)}{3^{2}-i^{2}}=\dfrac{6-2i}{9-i^{2}}=...$ Substitute $i^{2}$ with $-1$ and simplify: $...=\dfrac{6-2i}{9-(-1)}=\dfrac{6-2i}{9+1}=\dfrac{6-2i}{10}=\dfrac{6}{10}-\dfrac{2}{10}i=\dfrac{3}{5}-\dfrac{1}{5}i$
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