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)
