Let (z, w) (zw+wz)/2. Prove the following identities: (a) (z, w) + (iz, w) = |z||w| (b) |(z, w)| |z||w| (Cauchy-Schwarz inequality) (c) |zw||z| + w| + 2(z, w) (cosine law) = (d) z 0 and |z| = 0 if and only if z = 0 (e) |z|=(2, 2) (f) |zw|=|zw| 1