Let (z, w) (zw+wz)/2. Prove the following identities: (a) (z, w) + (iz, w) = |z||w|...

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

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