If `z=costheta+isintheta` is a root of the equation `a_0z^n+a_2z^(n-2)+.....+a_(n-1)z+a_n=0,` then prove that `a_0+a_1costheta+a_2^cos2theta++a_ncosntheta=0` `a_1"sin"theta+a_2^sin2theta++a_nsinntheta=0`

Explanation

To prove the given statements, we start with the polynomial equation:

\[ a_0 z^n + a_1 z^{n-1} + a_2 z^{n-2} + \ldots + a_{n-1} z + a_n = 0 \]

where \( z = \cos \theta + i \sin \theta \).

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