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: 62

Answer

$\dfrac{6+2i}{4-3i}=\dfrac{18}{25}+\dfrac{26}{25}i$

Work Step by Step

$\dfrac{6+2i}{4-3i}$ Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator: $\dfrac{6+2i}{4-3i}=\dfrac{6+2i}{4-3i}\cdot\dfrac{4+3i}{4+3i}=\dfrac{(6+2i)(4+3i)}{4^{2}-(3i)^{2}}=...$ $...=\dfrac{24+18i+8i+6i^{2}}{16-9i^{2}}=...$ Substitute $i^{2}$ by $-1$ and simplify: $...=\dfrac{24+18i+8i+6(-1)}{16-9(-1)}=\dfrac{24+26i-6}{16+9}=\dfrac{18+26i}{25}=...$ $...=\dfrac{18}{25}+\dfrac{26}{25}i$
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