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: 82

Answer

$z=a+bi$ So, $z-\frac{}{z}$ is a pure imaginary number.

Work Step by Step

$z=a+bi$ Find the conjugate of the complex numbers by changing the sign of their imaginary part: $\frac{}{z}=a-bi$ $z-\frac{}{z}=a+bi-(a-bi)=a+bi-a+bi=2bi$ Therefore, $z-\frac{}{z}$ is a pure imaginary number.
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