Question

sinx + icos2x and cosx – isin2x are conjugate to each other for ______.

Options

• x = nπ

• x = `(n + 1/2) pi/2`

• x = 0

• No value of x

Answer 1

sinx + icos2x and cosx – isin2x are conjugate to each other for x = 0.

Explanation:

Let z = sinx + icos2x

`barz` = sinx – icos2x

But we are given that `barz` = cosx – isin2x

∴ sinx – icos2x = cosx – isin2x

Comparing the real and imaginary parts, we get

sinx = cosx and cos2x = sin2x

⇒ tanx = 1 and tan2x = 1

⇒ tanx = `tan  pi/4` and  tan2x = `pi/4`

∴ x = `npi + pi/4`, n ∈ I and 2x = `npi + pi/4`

⇒ x = 2x

⇒ 2x – x = 0

⇒ x = 0