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(roots of unity) The extension of the real field to complex numbers ensures that any polynomial of degree n with real coefficients has n roots, as long as we allow roots to take complex values. Perhaps the simplest example of this is the polynomial x - 1, the roots of which are called the Nth roots of unity, and are given by {e2m/N, m = 0, 1, ..., N - 1}. (a) True or False j is a 4th root of unity. (b) True or False j is a 6th root of unity. (c) True or False j is an 8th root of unity. (d) Sketch the 8th roots of unity on the complex plane, labeling them in rectangular form a + bj as well as in polar form reº.

(roots of unity) The extension of the real field to complex numbers ensures that any polynomial of degree n with real coefficients has n roots, as long as we allow roots to take complex values. Perhaps the simplest example of this is the polynomial x - 1, the roots of which are called the Nth roots of unity, and are given by {e2m/N, m = 0, 1, ..., N - 1}. (a) True or False j is a 4th root of unity. (b) True or False j is a 6th root of unity. (c) True or False j is an 8th root of unity. (d) Sketch the 8th roots of unity on the complex plane, labeling them in rectangular form a + bj as well as in polar form reº.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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(roots of unity) The extension of the real field to complex numbers ensures that any polynomial of degree n with real coefficients has n roots, as long as we allow roots to take complex values. Perhaps the simplest example of this is the polynomial x - 1, the roots of which are called the Nth roots of unity, and are given by {e2m/N, m = 0, 1, ..., N - 1}. (a) True or False j is a 4th root of unity. (b) True or False j is a 6th root of unity. (c) True or False j is an 8th root of unity. (d) Sketch the 8th roots of unity on the complex plane, labeling them in rectangular form a + bj as well as in polar form reº.
Transcribed Image Text:(roots of unity) The extension of the real field to complex numbers ensures that any polynomial of degree n with real coefficients has n roots, as long as we allow roots to take complex values. Perhaps the simplest example of this is the polynomial x - 1, the roots of which are called the Nth roots of unity, and are given by {e2m/N, m = 0, 1, ..., N - 1}. (a) True or False j is a 4th root of unity. (b) True or False j is a 6th root of unity. (c) True or False j is an 8th root of unity. (d) Sketch the 8th roots of unity on the complex plane, labeling them in rectangular form a + bj as well as in polar form reº.
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