1-Define tan z = sin z/ cos z. Where is tan z defined and analytic? HINT: The Quo-tient Rule applies and analytic means continuously differentiable. Be sure to prove that theonly solutions to cos z = 0 are the real values

2-Suppose f : G ---- go to ----C is analytic and that G is open and connected. Prove that if f(z) is real for all z is member ofG, then f is constant. HINT: Use the Cauchy-Riemann equations.

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