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1. Whether or no Q∞ n=1(1 − z n ) converge absolutely and uniformly on compact subsets of ∆(1) ? If yes, tell which theorem is used. If yes, tell a reason. 2. Let f(z) be a branch of log 1+z 1−z . Find the power series of this function centered at the point z = 0 and find its radius of convergence. 3. Find a linear transformation f(z) that maps the points 1,2 and i to the points i, 1, 2, respectively. 4. Find a linear transformation T such that T({z ∈ C|Im(z) < 0}) = ∆(0, 2). 5. Find a power series for a function f(z) = 1 2z+1 at the point z = 2.

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Advanced Math Problems
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