Determine which of the following domains is simply connected. Justify your answer with a proof. (Hint: to prove that a domain is not simply connected, you may apply Cauchy's integral theorem, i.e. Theorem 9 in Section 4.4 of the textbook.)
(a) (3 points) {z=x+iy∈C∣∣xy∣<1}
(b) (3 points) {z∈C∣∣z²⁰²²∣>1}
(c) (3 points) The domain of the function f(z)=tanz