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CSIR NET Mathematics 2024| Complex Analysis | 20 April 2024
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Question 1
over the contour shown
Question 2
If f(z) is analytic on Δ, open unit disc such that f(0) = 0, |f(z)| < 1 for all z ∈ Δ, f(z) is analytic at z = 1 and f(z) = 1 . Then
Question 3
Consider the power series 
and 
and let r, s denote their radii of convergence respectively then
and and let r, s denote their radii of convergence respectively then
Question 4
Given a real number a > 0, consider the triangle 
with vertices 0, a, a + ia. If 
is given the counter clockwise orientation, then the contour integral 
(with Re(z) denoting the real part of z) is equal to
with vertices 0, a, a + ia. If is given the counter clockwise orientation, then the contour integral (with Re(z) denoting the real part of z) is equal to
Question 5Multiple Correct Options
Let D = 
and 
. Define 
by 
. Then which of the following are true?
and . Define by . Then which of the following are true?
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Apr 20CSIR NET & SET
