1. Consider the complex number z = -2(1 + i). (a) Compute z' by multiplying z by itself three times. (b) Compute z' using de Moivre's theorem and confirm that your answer is the same as the one you obtained in (a). (c) Using de Moivre's theorem, find the three cube roots of z.

1. Consider the complex number z = -2(1 + i). (a) Compute z' by multiplying z by itself three times. (b) Compute z' using de Moivre's theorem and confirm that your answer is the same as the one you obtained in (a). (c) Using de Moivre's theorem, find the three cube roots of z.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.4: Complex And Rational Zeros Of Polynomials

Problem 36E

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Question

1. Consider the complex number z = -2(1 + i).
(a) Compute z by multiplying z by itself three times.
(b) Compute z' using de Moivre's theorem and confirm that your answer is the
same as the one you obtained in (a).
(c) Using de Moivre's theorem, find the three cube roots of z.

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