2. (a) Show that (z − 1)(26 + 25 + 24 + z³ + z²+z+1) = z7 - 1. (b) Show that if ¢ is a 7th root if unity but $ # 1 then 5° +55 +5¹ +5³ +5² +5+ 1 = 0.
2. (a) Show that (z − 1)(26 + 25 + 24 + z³ + z²+z+1) = z7 - 1. (b) Show that if ¢ is a 7th root if unity but $ # 1 then 5° +55 +5¹ +5³ +5² +5+ 1 = 0.
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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Transcribed Image Text:2. (a) Show that (z − 1)(26 + 25 + 24 + 2³ + z² + z + 1) = z² − 1.
(b) Show that if ( is a 7th root if unity but ¢ ‡ 1 then
56 +55 +5¹ +5³ +5² + C + 1 = 0.
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