First slide

Algebra of complex numbers

Question

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

Moderate

A

$x = n π, n \in I$
B

$x = (n + \frac{1}{2}) π, n \in I$
C

$x = 0$
D

no value of $x .$

Solution

$\bar{\sin x + i \cos 2 x} = \cos x - i \sin 2 x$
$\begin{array}{l} \Rightarrow \sin x - i \cos 2 x = \cos x - i \sin 2 x \\ \Rightarrow \sin x = \cos x and \cos 2 x = \sin 2 x \\ \Rightarrow \tan x = 1 and \tan 2 x = 1 \end{array}$
These two equations cannot hold simultaneously.

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