Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 8 - Section 8.3 - Polar Form of Complex Numbers; De Moivre's Theorem - 8.3 Exercises - Page 610: 14

Answer

$|z|=1$ see graph below .
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Work Step by Step

See p. 602, Graphing Complex Numbers The complex plane is determined by the real axis and the imaginary axis. To graph the complex number a + bi, we plot the ordered pair of numbers (a,b) in this plane See p. 603, The modulus (or absolute value) of the complex number $z=a+bi$ is $|z|=\sqrt{a^{2}+b^{2}}$ ---------- Write z in the form a+bi: $z=\displaystyle \frac{-\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i$ Plot $(a,b)=(-\displaystyle \frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$ in the complex plane (see image, $\displaystyle \frac{\sqrt{2}}{2}\approx 0.707$). $|z|=\sqrt{(-\frac{\sqrt{2}}{2})^{2}+(\frac{\sqrt{2}}{2})^{2}}=\sqrt{\frac{1}{2}+\frac{1}{2}}=1$
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