Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises: 44

Answer

$\dfrac{-3+5i}{15i}=\dfrac{1}{3}+\dfrac{1}{5}i$

Work Step by Step

$\dfrac{-3+5i}{15i}$ Multiply the fraction by $\dfrac{-15i}{-15i}$: $\Big(\dfrac{-3+5i}{15i}\Big)\Big(\dfrac{-15i}{-15i}\Big)=\dfrac{45i-75i^{2}}{-225i^{2}}=...$ Substitute $i^{2}$ with $-1$: $...=\dfrac{-75(-1)+45i}{-225(-1)}=\dfrac{75+45i}{225}=\dfrac{75}{225}+\dfrac{45}{225}i=\dfrac{1}{3}+\dfrac{1}{5}i$
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