Question -
Answer -
Given:
(1 + i cos θ) / (1 –2i cos θ)
Z = (1 + i cos θ) / (1– 2i cos θ)
Let us multiply anddivide by (1 + 2i cos θ)
For a complex numberto be purely real, the imaginary part should be equal to zero.
So,
3cos θ = 0(since, 1 + 4cos2θ ≥ 1)
cos θ = 0
cos θ = cos π/2
θ = [(2n+1)π] / 2, forn ∈ Z
= 2nπ ± π/2, for n ∈ Z
∴ The values of θto get the complex number to be purely real is 2nπ ± π/2, for n ∈Z