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CSIR NET Mathematics 2024| Complex Analysis | 06 April 2024
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Question 1
Let C be the counter-clockwise oriented circle of radius 
centred at i = 
. Then the value of the contour integral 
, is
centred at i = . Then the value of the contour integral , is
Question 2Multiple Correct Options
Let D = 
and 
. Define 
by 
. Then which of the following are true?
and . Define by . Then which of the following are true?
Question 3
For any complex valued function f let Df denote the set on which the function f satisfies Cauchy-Riemann equations. Identify the functions for which Df is equal to ℂ .
Question 4Multiple Correct Options
Consider the function f(z) = 
for 0 < |z| < 1 where m n are positive integers. Then z _ Q Is
for 0 < |z| < 1 where m n are positive integers. Then z _ Q IsQuestion 5
For 
, let 
. Which of the following are true?
, let . Which of the following are true?
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Apr 6CSIR NET & SET
