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 

See also  Solve Number Theory Mcqs | Number Theory Mcqs with solution
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