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The complex number sin(x)+icos(2x) and c...

The complex number `sin(x)+icos(2x)` and `cos(x)-isin(2x)` are conjugate to each other for

A

`x = npi, n in Z`

B

`x= 0`

C

`x = (n+1//2)pi, n in Z`

D

no value of x

Text Solution

Verified by Experts

The correct Answer is:
D
Let `z_(1) = sin x + i cos 2x = cos x - i sin 2x`
Then `barz_(1) = z_(2)`
`rArr sin x - i cos 2x = cos x - i isn 2x `
`rArr sin x = cos x and cos 2x = sin 2x`
`rArr tan x = 1 and tan 2x = 1`
`rArr x = (pi)/(4) and x = (pi)/(8)`
This is not possible.
Hence, there is no value of x.
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