Define tan z = sin z/ cos z. Where is tan z defined and analytic

| August 30, 2017

Question
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 the only 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 of G, then f is constant. HINT: Use the Cauchy-Riemann equations.

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