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: 60

Answer

$\dfrac{3i}{5+i}=\dfrac{3}{26}+\dfrac{15}{26}i$

Work Step by Step

$\dfrac{3i}{5+i}$ Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator: $\dfrac{3i}{5+i}=\dfrac{3i}{5+i}\cdot\dfrac{5-i}{5-i}=\dfrac{3i(5-i)}{5^{2}-i^{2}}=\dfrac{15i-3i^{2}}{25-i^{2}}=...$ Substitute $i^{2}$ by $-1$ and simplify: $...=\dfrac{15i-3(-1)}{25-(-1)}=\dfrac{15i+3}{25+1}=\dfrac{3+15i}{26}=\dfrac{3}{26}+\dfrac{15}{26}i$
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