3.(a) Show that z8 − 1 = (z − 1)(z + 1)(z − i)(z + i)q(z) for some polynomial q(z) which you should determine. (b) [ACS] Show that the following holds: if (is an eighth root of unity but ¢ ‡ 1,−1, i, –i then Ǫ + AC³ + BC² + CC + D = 0. Here A, B, C, D are certain integers which you should find.
3.(a) Show that z8 − 1 = (z − 1)(z + 1)(z − i)(z + i)q(z) for some polynomial q(z) which you should determine. (b) [ACS] Show that the following holds: if (is an eighth root of unity but ¢ ‡ 1,−1, i, –i then Ǫ + AC³ + BC² + CC + D = 0. Here A, B, C, D are certain integers which you should find.
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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q3
![3.(a) Show that z³ − 1 = (z − 1)(z + 1)(z − i)(z + i)q(z) for some polynomial q(z) which you should
determine.
(b) [ACS] Show that the following holds: if is an eighth root of unity but ¢ ‡ 1,−1, i, -i then
Ǫ + AC³ + BC² + CÇ + D = 0. Here A, B, C, D are certain integers which you should find.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F490cbcd2-ad81-426b-824f-903aced284ba%2Fac190581-a906-4b27-a8ee-2b6b2a0e5713%2F2j0lxmd_processed.png&w=3840&q=75)
Transcribed Image Text:3.(a) Show that z³ − 1 = (z − 1)(z + 1)(z − i)(z + i)q(z) for some polynomial q(z) which you should
determine.
(b) [ACS] Show that the following holds: if is an eighth root of unity but ¢ ‡ 1,−1, i, -i then
Ǫ + AC³ + BC² + CÇ + D = 0. Here A, B, C, D are certain integers which you should find.
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