Complex Analysis MCQs Test 02

COMPLEX-ANALYSIS MCQS

Complex Analysis MCQs  test 02 consist of multiple choice questions.In this test, there are 61 questions. Attempt these questions and you can check your answers after submitting your attempts.

 attempt other multiples, then click on mcqs 01.

complex analysis definitions are available. Click Here or Notes

For quick review and full solutions


  1. Click on Complex Numbers, Properties of i and Algebra of complex numbers with full detail.
  2. Click on Complex plane, Modulus, Properties of modulus and Argand Diagram with full detail.
  3. Click on Conjugate of a complex number with full detail.
  4. Click on Polar form of a complex number with full detail.
  5. Click on Cube roots of a complex Number with full detail




Complex Analysis MCQs

1. If \int_{C} Z^n dz=0 then C is

 
 
 
 

2. (-1)^{2i} =

 
 
 
 

3. Modulus of 4+3i is

 
 
 
 

4. Z is purely imaginary if and only if

 
 
 
 

5. Product of complex number Z and conjugate is

 
 
 
 

6. Piece wise smooth curve is also known as

 
 
 
 

7. A function which is analytic everywhere in a complex plane is known as

 
 
 
 

8. which of the following is entire function

 
 
 
 

9. If C is a circle at Zo with radius r then \int_{C} (Z-Z_0) dz=

 
 
 
 

10. If Z= x+iy then |sin z|^2=

 
 
 
 

11. Z= rcosθ+i rsinθ  is known as

 
 
 
 

12. tan^{-1}(1)=

 
 
 
 

13. Log(i-1)=

 
 
 
 

14. A part of many complex valued function which is single valued and analytic is known as

 
 
 
 

15. Log (i)=

 
 
 
 

16. e^{log(1+i)}  =

 
 
 
 

17. A Curve traced by complex valued function x=f(z) s.t f(z1)≠f(z2) for z1≠z2 then curve is known as

 
 
 
 

18. which of the following is analytic

 
 
 
 

19. i^{n}\times i^{2n}\times i^{3n}\times i^{4n}= \\ \forall n \in Z

 
 
 
 

20. If a function is not analytic at Z=a then Z=a is known as

 
 
 
 

21. A function which has poles as its only singularities in the finite part of the plane is known as

 
 
 
 

22. A curve which is simple as well as closed is known as

 
 
 
 

23. which of the following is entire function

 
 
 
 

24. Every entire bounded function is

 
 
 
 

25. i^{1 \times n} + i^{2 \times n} +i^{3 \times n} +i^{4 \times n}=\\ \forall n \in Z

 
 
 
 

26. If Z= a+ib then Re(Z)=

 
 
 
 

27. cos(lna)+ isin(lna)=      ?            for all a>0 then

 
 
 
 

28. tan^{-1}(1)=

 
 
 
 

29. if Z=rcosθ+irsinθ then cosθ=

 
 
 
 

30. Product of four consecutive powers of i is

 
 
 
 

31. which of the following is a kind of singularity

 
 
 
 

32. i^{n}+i^{2n}+i^{3n}+i^{4n}=\\ \forall n \in Z

 
 
 
 

33. i^{15}+ i^{16}+i^{17}+i^{18}=

 
 
 
 

34. If C is a circle at Zo with radius r then \int_{C} (Z-Z_0)^{-1}dz=

 
 
 
 

35. Sum of four consecutive four multiple  powers of i is

 
 
 
 

36. i^{4}+i^{8}+i^{12}+i^{16}=

 
 
 
 

37. (-i)^i =

 
 
 
 

38. e^{-\pi/4}+i\frac{log2}{2}=

 
 
 
 

39. (i)^i=

 
 
 
 

40. Sum of consecutive four powers of i is

 
 
 
 

41. If Z= x+iy then |cos z|^2=

 
 
 
 

42. If Z is a complex number thrn log Z

 
 
 
 

43. i^{1+n}+i^{2+n}+i^{3+n}+i^{4+n}=?\,\,\,\, \forall n \in Z

 
 
 
 

44. Let f(Z) be a complex valued function defined on a domain D s.t a ε D . If f(a)=0  then Z=a is known as

 
 
 
 

45. Z is purely real if and only if

 
 
 
 

46. Conjugate of Z= 4+5i

 
 
 
 

47. i^{16} \times i^{17} \times i^{18} \times i^{19} =

 
 
 
 

48. Let f(Z) be analytic in a simply connected domain D in a closed continuous curve then \int_{C}f(Z)dz=0 is the statement of

 
 
 
 

49. Log i =

 
 
 
 

50. If Z= a + ib then Im(Z)=

 
 
 
 

51. product of four Consecutive multiple powers of i is

 
 
 
 

52. Z+\overline{Z}=

 
 
 
 

53. \int_{0}^{\pi} \frac{1}{Z}dz=

 
 
 
 

54. rcosθ + i sinθ =

 
 
 
 

55. Z-\overline{Z}=

 
 
 
 

56. If C is a straight line from Z= -i to Z=i then \int_{C}|Z|dz=

 
 
 
 

57. If C is a circle with |Z|= 2 then \int_{C}\frac{dz}{z^2-1}=

 
 
 
 

58. Which formula is used for Euler’s Identity

 
 
 
 

59. A function is analytic if it is a function of

 
 
 
 

60. tan(ArgZ)=

 
 
 
 

61. Which of the following is not analytic function

 
 
 
 




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