Using results

(i)	R5298: Complex conjugatation is an additive operation
(ii)	R3429: Complex conjugation is a multiplicative operation
(iii)	R2950: Complex conjugation operation is an involution

we have \begin{equation} \sum_{n = 1}^N z_n \overline{w}_n = \sum_{n = 1}^N \overline{\overline{z}_n w_n} = \overline{\sum_{n = 1}^N \overline{z}_n w_n} \end{equation} $\square$