CSIR-NET Mathematical Science - Complex Analysis MCQ - Attempt Here!

By Astha Singh|Updated : July 1st, 2022

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Multiple Choice Questions On Complex Analysis

Question 1.
Let C denote the positively oriented boundary of the square whose sides lie along the line Let then

2π
π/8
-4π
None Of These

Question 2.

find the residue of

at its essential singularity

21/22
22/23
23/24
24/25

Question 3.

Let

then

f has a pole of order 2 at z=0
f is analytic function at z=0
where the integral is taken anticlockwise
The residue of f at z=0 is

Question 4.

Let

then

The number of zeros of f(z) in |z|<1 is 2022
The number of zeros of f(z) in |z|<1 is 1011
All the zeros of f(z) are simple.
All the zeros of f(z) are need not be simple.

Question 5.

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

|f’(1)| = 1
|f’(x)| < 1

Question 6.

For any complex valued function f let D_f denote the set on which the function f satisfies Cauchy-Riemann equations. Identify the functions for which D_f is equal to ℂ .