 # Problem 1: Compute (i.e. evaluate real and imaginary parts) arccos...

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Problem 1: Compute (i.e. evaluate real and imaginary parts) arccosh (2i) Problem 3: Consider the following two linear fractional transformations = + + 2 - + i f2(z) = - is - + 1 + - i Compute Problem 4: Find a linear fractional transformation for : Cx Cx that maps the unit circle S1:= {z:/2|=1} on itself and fo(i/2) = 0, fo(i) = 1. Hint: If you missed the last class, please check out the Problem book - Problem #190. Problem 2: Compute (i.e. evaluate real and imaginary parts) arctan (1+2i) Problem 5: Find a linear fractional transformation fo : Cx Cx that maps the upper half plane of C onto the unit disc D := { z : < 1}, such that fo(i) = 0 and for a given real number T € R, T # 0, we also have fo(r) = 1. Hint: If you missed the last class, ploase check out the Problem book - Problem #182.

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