30. If x = cos θ + isin θ, then the value of x^n − 1/x^n=
A. 2isin nx
B. 2i cos nx
C. 2 cos nx
D. 2 sin nx
31. If |z| = r and arg(z) = θ, then all the nth roots of z are:
A. r^1/n cis( 2kπ+θ/n )
B. r^1/n cis( 2π+θ/kn )
C. r°1/n cis( 2π+kθ/n )
D. r^1^n cis( 2kπ+θ/kn )
32. 1, ω, ω2 , …, ωn^−1 are nth roots of:
A. zero
B. unity
C. 2i
D. None of these
33. If z is a root of w, then which of following is also a root of w?
A. 1
B. −z
C. z̅
D. z −1
34. Three cube roots of 8i are:
A. 2, 2ω, 2ω^2
B. 2i, 2iω, 2iω^2
C. −2, −2ω, −2ω^2
D. −2i, −2iω, −2iω^2
35. Sum of four fourth roots of unity is:
A. 0
B. 1
C. i
D. −1
36. (cos θ+isin θ)^n/(cos φ+isin φ)^m equals:
A. cos(mθ + nφ) + isin(mθ + nφ)
B. cos(nθ + mφ) + isin(nθ + mφ)
C. cos(mθ − nφ) + isin(mθ − nφ)
D. cos(nθ − mφ) + isin(nθ − mφ)
37. (cos α−isin α) 11 (cos β+isin β) 9 equals:
A. cos(11α + 9β) + isin(11α + 9β)
B. cos(11α − 9β) + isin(11α − 9β)
C. cos(−11α + 9β) + isin(−11α + 9β)
D. cos(−11α − 9β) + isin(−11α − 9β)
38. For a complex number z, e^iz−e^−iz /i(e^iz+e^−iz) =
A. cot z
B. tan z
C. coth z
D. tanh z
39. sin2 z + cos2 z=
A. 1
B. −1
C. 0
D. 2 sin z cos z
