Question

The complex numbers sinx+icos2x and cosx-isin2x are conjugate to each other for

• A.
• B.
• C. x=0
• D. No value of x

Answer 1

The correct option is D

No value of x

sinx+icos2x and cosx-isin2xare conjugate to each other if sinx=cosx and cos2x=sin2x

Or tan x = 1 ⇒ x = $\frac{\pi }{4}$,$\frac{5\pi }{4}$,$\frac{9\pi }{4}$, .......... ...............(i)

And tan 2x = 1 ⇒ 2x = $\frac{\pi }{4}$,$\frac{5\pi }{4}$,$\frac{9\pi }{4}$, ..........

or x = $\frac{\pi }{8}$,$\frac{5\pi }{8}$,$\frac{9\pi }{8}$, .......... ...............(ii)

There exists no value of x common in (i) and (ii). Therefore there is no value of x for which the given complex numbers are conjugate.