I know I have to use the definition of the modulus in terms of the function times its complex conjugate, and the Cauchy product of two power series, but I do not know how to continue.

Let $f (z) = ?_{k = 0}^{n} a_{k} z^{k}$ be a complex polynomial $(a_{i} ? C)$ of degree $n > 0$ . Prove $\frac{1}{2 ?i} ?_{? z ? = R} z^{n ? 1} ? f (z) ?^{2} d z = a_{0} \overset{a}{?}_{n} R^{2 n}$

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I know I have to use the definition of the modulus in terms of the function times its complex conjugate, and the Cauchy product of two power series, but I do not know how to continue.
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student submitted image, transcription available below

Let

f (z) = ?_{k = 0}^{n} a_{k} z^{k}

be a complex polynomial

(a_{i} ? C)

of degree

n > 0

. Prove

\frac{1}{2 ?i} ?_{? z ? = R} z^{n ? 1} ? f (z) ?^{2} d z = a_{0} \overset{a}{?}_{n} R^{2 n}

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