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: 57

Answer

$\dfrac{7}{4+3i}=\dfrac{28}{25}-\dfrac{21}{25}i$

Work Step by Step

$\dfrac{7}{4+3i}$ Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator: $\dfrac{7}{4+3i}=\dfrac{7}{4+3i}\cdot\dfrac{4-3i}{4-3i}=\dfrac{7(4-3i)}{4^{2}-(3i)^{2}}=\dfrac{7(4-3i)}{16-9i^{2}}=...$ Substitute $i^{2}$ with $-1$ and simplify: $...=\dfrac{7(4-3i)}{16-9(-1)}=\dfrac{7(4-3i)}{16+9}=\dfrac{28-21i}{25}=\dfrac{28}{25}-\dfrac{21}{25}i$
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