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: 38

Answer

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

Work Step by Step

$\dfrac{1}{1+i}$ Multiply the fraction by $\dfrac{1-i}{1-i}$ $\Big(\dfrac{1}{1+i}\Big)\Big(\dfrac{1-i}{1-i}\Big)=\dfrac{1-i}{1-i^{2}}=...$ Since $i^{2}=-1$, the equation becomes: $...=\dfrac{1-i}{1-(-1)}=\dfrac{1-i}{2}=\dfrac{1}{2}-\dfrac{1}{2}i$
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