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: 45

Answer

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

Work Step by Step

$\dfrac{1}{1+i}-\dfrac{1}{1-i}$ Evaluate the substraction: $\dfrac{1}{1+i}-\dfrac{1}{1-i}=\dfrac{(1-i)-(1+i)}{1-i^{2}}=\dfrac{1-i-1-i}{1-i^{2}}=\dfrac{-2i}{1-i^{2}}$ Substitute $i^{2}$ with $-1$: $...=\dfrac{-2i}{1-(-1)}=\dfrac{-2i}{2}=-i$
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