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  4. If x + (1/x) = 2 cos θ, then for any integer n, xn + (1/xn) =

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Q. If $x + \frac{1}{x} = 2\,\cos\,\theta$, then for any integer $n$, $x^{n} + \frac{1}{x^{n}} = $

WBJEEWBJEE 2011Complex Numbers and Quadratic Equations

Solution:

Let $ x= \cos \theta+i \sin \theta $
Then, $ \frac{1}{x}=\cos \theta-i \sin \theta $
$\therefore x+\frac{1}{x}=2 \cos \theta $
$\Rightarrow x^{n}+\frac{1}{x^{n}}=2\, \cos\, n \theta$