MCQS

# Complex Numbers MCQS With Solution | Solve Complex Numbers MCQS

51. The value of Log(−i) is:

A. π/2 i

B. 3π/2 i

C. − π/2 i

D. − 3π/2 i

52. If x is any negative real number, then Logx is:

A. ln x + iπ

B. ln x − iπ

C. ln(−x) + iπ

D. ln(−x) − iπ

53. log(e^z )=

A. z

B. z + 2nπ

C. z + 2nπi

D. e^z

54. If z is a positive real number, then

A. Log(z)=log(z)

B. Log(z)=log(z)+ 2nπ

C. log(z)=Log(z)+ 2nπ

D. None of these

55. sinh^−1 z=

A. log(z + √ z^2 + 1)

B. log(z − √ z^2 + 1)

C. log(z + √ z^^2 − 1)

D. log(z − √ z^2 − 1)

56. cosh^−1 z=

A. log(z + √ z^2 + 1)

B. log(z − √ z^2 + 1)

C. log(z + √ z^2 − 1)

D. log(z − √ z^2 − 1)

57. sin^−1 z=

A.   ilog(iz + √ 1 + z^2 )

B. −i log(iz − √ 1 − z^2 )

C. −ilog(iz + √ 1 + z^2 )

D. −i log(iz + √ 1 − z^2 )

58. If z and w are complex numbers, then z^w=

A. exp(z log w)

B. z exp(log w)

C. exp(w log z)

D. w exp(log z)

59. If z and w are complex numbers, then the principal value of z^w is:

A. exp(zLogw)

B. z exp(Logw)

C. exp(wLogz)

D. w exp(Logz)

60. The principal value of i^i is:

A. e^π/2

B. −e^π/2

C. e −^π/2

D. −e −^π/2

61. The principal value of (−1)^i is:

A. e^π

B. e^−π

C. −e^π

D. −e^−π

62. The principal value of (−i)^−i is:

A. e^π/2

B. −e^π/2

C. e^− π/2

D. −e^− π/2

63. If a is a positive real number, then the principal value of a i is:

A. cos(ln a) + isin(ln a)

B. cos(a) + isin(a)

C. sin(a) + i cos(a)

D. sin(ln a) + i cos(ln a)