Question: Let V be a complex inner product space. Prove that, for all z, w 6 V, (a) ||z + w||2 = ||z||2 + 2 Re(z.

Let V be a complex inner product space. Prove that, for all z, w 6 V,
(a) ||z + w||2 = ||z||2 + 2 Re(z. w) + ||w||2;
(b) (z, w) = 1/4(||z + xv||2 - ||z - w||2
+ i ||z + i w||2 - i ||z - i w||2).

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