Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Consider the calculation

Consider the calculation

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Please send your answer by word
0.4 Consider the calculation of roots of the equation z=a where N >1 is an integer and a = ale a nonzero complex number. (a) First verify that there are exactly N roots for this equation and that they are given by Zk =rel where r = |a|N and Og = (0 +2xk)/N for k =0, 1,..., N- 1. (b) Use the above result to find the roots of the following equations: (i) z? = 1, (ii) z? = –1, (iii) z' = 1, (iv) z' = –1, and plot them in a polar plane (i.e., indicating their magnitude and phase). Explain how the roots are distributed in the polar plane. Answers: Roots of z = -1= le* are zg = lel(+2xk)/, k = 0, 1, 2, equally spaced around circle of radius r.
Transcribed Image Text:0.4 Consider the calculation of roots of the equation z=a where N >1 is an integer and a = ale a nonzero complex number. (a) First verify that there are exactly N roots for this equation and that they are given by Zk =rel where r = |a|N and Og = (0 +2xk)/N for k =0, 1,..., N- 1. (b) Use the above result to find the roots of the following equations: (i) z? = 1, (ii) z? = –1, (iii) z' = 1, (iv) z' = –1, and plot them in a polar plane (i.e., indicating their magnitude and phase). Explain how the roots are distributed in the polar plane. Answers: Roots of z = -1= le* are zg = lel(+2xk)/, k = 0, 1, 2, equally spaced around circle of radius r.
Expert Solution
steps

Step by step

Solved in 5 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS