(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 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 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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

(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 {ej2m/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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