# Complex Analysis MCQ - Attempt Quiz Here!

By Astha Singh|Updated : August 30th, 2022

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## 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

Question 2. Given a real number a > 0, consider the triangle  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

1. 0
2. ia2
##### Question 3. Let  be an entire function such that . Then which of the following is true?
1. f is constant
2. f can have infinitely many zeros
3. f can have at most finitely many zeros
4. 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?

1.  is infinitely differentiable
2. u is continuous but need not be differentiable
3. u is bounded
4. f can be represented by an absolutely convergent power series  for all z

Question 5. Let  be the positively oriented circle of radius 2 centered at the origin. The value of  for which

1.  = –1/3
2.  = 0
3.  = 1/3
4.  = 1

Question 6. Let C be the counter-clockwise oriented circle of radius  centred at i = . Then the value of the contour integral , is

Question 7. 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
1. 0
2. ia2
Question 8. Let  be an entire function such that . Then which of the following is true?
1. f is constant
2. f can have infinitely many zeros
3. f can have at most finitely many zeros
4. f is necessarily nowhere vanishing
Question 9. 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?
1.  is infinitely differentiable
2. u is continuous but need not be differentiable
3. u is bounded
4. f can be represented by an absolutely convergent power series  for all z
Question 10. Let D =  and . Define  by . Then which of the following are true?
1. F is one to one
2. F is not one to one
3. F is onto
4. 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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