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If the complex numbers sinx+icos 2x and ...

If the complex numbers `sinx+icos 2x` and `cosx-isin2x` are conjugate of each other, then the number of values of x in the inverval `[0, 2pi)` is equal to (where, `i^(2)=-1`)

A

0

B

1

C

2

D

3

Text Solution

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The correct Answer is:
To solve the problem, we need to determine the values of \( x \) in the interval \( [0, 2\pi) \) for which the complex numbers \( z_1 = \sin x + i \cos 2x \) and \( z_2 = \cos x - i \sin 2x \) are conjugates of each other. ### Step 1: Set up the equation for conjugates Since \( z_2 \) is the conjugate of \( z_1 \), we have: \[ z_2 = \overline{z_1} \] This means: \[ \cos x - i \sin 2x = \sin x - i \cos 2x \]
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