MCQS

# Complex Numbers MCQS With Solution | Solve Complex Numbers MCQS

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.

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

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