Complex NumbersHard

Question

The complex numbers sin x + i cos 2x and cos x - i sin 2x are conjugate to each other, for

Options

A.x = nπ
B.x = 0
C.
D.no value of x

Solution

sin x + i cos2x = cos x + i sin2x
⇒    cos2x = sin2x
tan x = 1    &    tan 2x = 1
  
∵  both equation will not have solution simultaneously.

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