Question

The real value of θ for which the expression (1 + icos θ)/(1 - 2icosθ) is a real number is:

A. nπ + π/4
B. nπ + (-1)ⁿ π/4
C. 2nπ ± π/2
D. none of these

Answer 1

Let z = (1 + icos θ)/(1 - 2icosθ)

Rationalizing the denominator,

⇒ 3 cos θ = 0

⇒ cos θ = 0

∴ θ = (2n + 1) π/2, n ∈ N