Multiple Choice Questions On Complex Analysis
Question 1. Let C be the counter-clockwise oriented circle of radius 
centred at i = 
. Then the value of the contour integral 
, is
with vertices 0, a, a + ia. If 
is given the counterclockwise orientation, then the contour integral 
(with Re(z) denoting the real part of z) is equal to- 0
- ia2
Question 3. Let be an entire function such that . Then which of the following is true?
- f is constant
- f can have infinitely many zeros
- f can have at most finitely many zeros
- f is necessarily nowhere vanishing
Question 4. Let f(z) = (z3 + 1) sin z2 for z 
. Let f(z) = u(x, y) + i v (x, y), where z = x + iy and u, v are real valued functions. Then which of the following are true?
- is infinitely differentiable
- u is continuous but need not be differentiable
- u is bounded
- f can be represented by an absolutely convergent power series for all z
is infinitely differentiable
for all z 
Question 5. Let 
, 
be the positively oriented circle of radius 2 centered at the origin. The value of 
for which 
- = –1/3
- = 0
- = 1/3
- = 1
= –1/3
= 0
= 1/3
= 1Question 6. Let C be the counter-clockwise oriented circle of radius 
centred at i = 
. Then the value of the contour integral 
, is
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- 0
- ia2
be an entire function such that 
. Then which of the following is true?- f is constant
- f can have infinitely many zeros
- f can have at most finitely many zeros
- f is necessarily nowhere vanishing
. Let f(z) = u(x, y) + i v (x, y), where z = x + iy and u, v are real valued functions. Then which of the following are true?- is infinitely differentiable
- u is continuous but need not be differentiable
- u is bounded
- f can be represented by an absolutely convergent power series for all z
is infinitely differentiable
for all z 
and 
. Define 
by 
. Then which of the following are true?- F is one to one
- F is not one to one
- F is onto
- F is not onto
| Answer Keys for Complex Analysis | |
| Question Number | Answer Key |
| 1 | A |
| 2 | B |
| 3 | C |
| 4 | A & B |
| 5 | B, C & D |
| 6 | A |
| 7 | B |
| 8 | C |
| 9 | B & C |
| 10 | A & C |
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