1. Let z reie and w Reip. Prove that = = Re · w+z w z - = R² - 1² R²-2Rr cos (0) + r²²
1. Let z reie and w Reip. Prove that = = Re · w+z w z - = R² - 1² R²-2Rr cos (0) + r²²
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:1. Let z =
reie and w Reip. Prove that
Re
(@+ ²)
R²²
R22Rr cos (0
·0) + r².
2. (a) Calculate (i+1)302 + (i-1)302 and write it in the form of x + iy.
(b) Find an upper and lower bound for |z − 2i| if |z − 1| ≤ 1.
-
(c) Find a lower and upper bound for
if |z − 1| ≤ 1.
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