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 - Page 64: 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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.