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N-1 Σe²rijk/N = 0 j=0 when 0

N-1 Σe²rijk/N = 0 j=0 when 0

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
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Please do Exercise 7 part A,B,C and show step by step and explain

N-1 Σe²rijk/N = 0 j=0 when 0 <k < N. Exercise 7. (a) Equation (3) does not include the case k = 0. What result do you get for the sum eijk/N when k=0? (b) Show that the result of part (a) can be combined with Equation (3) to give an equation of the form: N-1 e2rijk/N = C-8k0 when 0 ≤ k < N, (3) N-1 j=0 and give the value of the constant C. (c) Use your result from(b) to simplify the expression EN-¹e2ij(k-m)/N, where m is an integer such that 0 <m<N.
Transcribed Image Text:N-1 Σe²rijk/N = 0 j=0 when 0 <k < N. Exercise 7. (a) Equation (3) does not include the case k = 0. What result do you get for the sum eijk/N when k=0? (b) Show that the result of part (a) can be combined with Equation (3) to give an equation of the form: N-1 e2rijk/N = C-8k0 when 0 ≤ k < N, (3) N-1 j=0 and give the value of the constant C. (c) Use your result from(b) to simplify the expression EN-¹e2ij(k-m)/N, where m is an integer such that 0 <m<N.
Expert Solution
Introduction

As per the question we are given a partial sum involving the exponential of complex number sequence. And using that we have to show :

  1. Find the value of the sum for k = 0
  2. Using the solution (a) we have to show that the sum can be written as C δk0  for some constant C which we have to find.
  3. Using the solution (b) we have to simplify another summation involving (k-m) instead of k

 

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