Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.2 Trigonometric (Polar) Form of Complex Numbers - 8.2 Exercises - Page 372: 72

Answer

$z$ and $iz$ have the same absolute value. $z$ and $iz$ are perpendicular to each other with the same absolute value.

Work Step by Step

Let $z = a + bi$ The absolute value of $z$ is $\sqrt{a^2 + b^2}$ Now, $iz = i(a + bi) = bi^2 + ai = -b + ai$ (since $i^2 = -1$) The absolute value of $iz$ is $\sqrt{(-b)^2 + a^2}$ = $\sqrt{a^2 + b^2}$ Therefore, $z$ and $iz$ have the same absolute value. $z$ and $iz$ are perpendicular to each other with the same absolute value.
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.