2. Let be a real number such that 0 < 0 < 27. Let n be a positive integer. (a) Show that for each complex number z ‡ 1, (b) Show that n n Σzk k=0 k=0 Text = 1-2n+1 1-z Σcos(k0) = Re (Σ (eig)* ( 2 (~²9)*).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. Let be a real number such that 0 < 0 < 2π. Let n be a positive integer.
(a) Show that for each complex number z ‡ 1,
(b) Show that
n
k=0
n
k=0
zk
Trett
=
1 — zn+1
1-z
cos(ke) = Re
k
(e²ogja).
n
Σ (eo)'
k=0
Transcribed Image Text:2. Let be a real number such that 0 < 0 < 2π. Let n be a positive integer. (a) Show that for each complex number z ‡ 1, (b) Show that n k=0 n k=0 zk Trett = 1 — zn+1 1-z cos(ke) = Re k (e²ogja). n Σ (eo)' k=0
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