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: 30


$(\sqrt 2,135)$

Work Step by Step

To do these argument problems we first need to look at the coefficients of both the real and non-real/imaginary parts. Then we approach the problem using our beloved $cis(x) = cos(x) + i(sin(x))$. When we do this we want to match the coefficients to unit circle values. This can be done by multiplying by 1/r which will be part of our final argument in the form (r, theta). So here we have coefficients of (1,-1). When we multiply by $1/\sqrt 2$ we get the unit circle value of ($1/\sqrt 2$,$-1/\sqrt 2$) at 135 degrees. So 1/r is equal to $\sqrt 2$ and theta is 45 degrees so the answer is... $(\sqrt 2,135)$
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