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Application of Schwarz Lemma--Complex Analysis Let f be holomorphic in D = {z: |z| < 1} and suppose that |f(z)| ≤ M for all z in D. If f(z_{k}) = 0 for 1 ≤ k ≤ n, show that |f(z)| ≤ M \prod |z - z_{k}|/|1 - \bar{z_{k}}z| for k = 1 to n and |z| < 1. I am just very confused about...

Homework Statement Given that z_{1}z_{2} ≠ 0, use the polar form to prove that Re(z_{1}\bar{z}_{2}) = norm (z_{1}) * norm (z_{2}) \Leftrightarrow θ_{1} - θ_{2} = 2n∏, where n is an integer, θ_{1} = arg(z_{1}), and θ_{2} = arg(z_{2}). Also, \bar{z}_{2} is the conjugate of z_{2}. Homework...