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The complex number sinx+icos2x and cosx-...

The complex number `sinx+icos2x` and `cosx-isin2x` are conjugate to each other when

A

`x=npi`

B

x=0

C

`x=(n+1/2)pi`

D

no value of x

Text Solution

Verified by Experts

The correct Answer is:
D
Since (sin x+ I cos2 x )=cos x - I sin 2x
`rArr ` sin x- icos 2x =cos x -I sin 2x
`rArr` sin x= cos x and cos 2 x = sin 2x
`rArr ` tan x=1 and tan 2x=1
`rArr x=pi//4 and pi//8 ` which is not possible at same time .
Hence no solution exists.
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