Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
(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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question

more details, handwrite

**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 \(x^N - 1\), the roots of which are called the \(N\)th roots of unity, and are given by \(\left\{ e^{j2\pi m/N}, \, m = 0, 1, \ldots, N-1 \right\}\). (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 \(re^{j\theta}\).
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 \(x^N - 1\), the roots of which are called the \(N\)th roots of unity, and are given by \(\left\{ e^{j2\pi m/N}, \, m = 0, 1, \ldots, N-1 \right\}\). (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 \(re^{j\theta}\).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Different Types of System and Its Property
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS