a) Find an analytic function (or functions) if 2 Ref(Z) = x ² = y ²² + 2 x and fli) = 2i - 1 b) Find all the analytic functions for which Rez = Im f(z)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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4) a) Find an analytic function (or functions) if
Reflz) = x²_y² + 2x and fli) = 2i-1
b) Find all the analytic functions for which
Rez = Im f(z)
5) Using Ex 9.5 from Lecture Notes determine which of the
following functions are entire. Justify your answer:
i) cos 1214
iv) Rez
ii) z²_4iz²³+ (1+8₁) z + (17 +i√z)
iii) z Rez
v) Imz
vi) i Rez
Transcribed Image Text:4) a) Find an analytic function (or functions) if Reflz) = x²_y² + 2x and fli) = 2i-1 b) Find all the analytic functions for which Rez = Im f(z) 5) Using Ex 9.5 from Lecture Notes determine which of the following functions are entire. Justify your answer: i) cos 1214 iv) Rez ii) z²_4iz²³+ (1+8₁) z + (17 +i√z) iii) z Rez v) Imz vi) i Rez
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