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If we represent the sum of the series by the complex exponential form show that a cos wt + acos (wt + 8) + acos (wt +28) + + acos [wt+ (n − 1)8] z = ae(1+ei+e¹²6 +...+ei(n-1)6) zz: sin²n8/2 sin² 8/2

If we represent the sum of the series by the complex exponential form show that a cos wt + acos (wt + 8) + acos (wt +28) + + acos [wt+ (n − 1)8] z = ae(1+ei+e¹²6 +...+ei(n-1)6) zz: sin²n8/2 sin² 8/2

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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Problem 1.19 If we represent the sum of the series a cos wt + a cos (wt + 6) + a cos (wt + 26) + · … · + a cos [wt + (n – 1)8] by the complex exponential form z = aci (1 + e® + e'26 + ... +ein-1)6) show that sin² n8/2 sin? 8/2 zz* =
Transcribed Image Text:Problem 1.19 If we represent the sum of the series a cos wt + a cos (wt + 6) + a cos (wt + 26) + · … · + a cos [wt + (n – 1)8] by the complex exponential form z = aci (1 + e® + e'26 + ... +ein-1)6) show that sin² n8/2 sin? 8/2 zz* =
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