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.
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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.
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