The following is from part of an undergrad complex analysis [practice] midterm. What do people think?
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Consider the functions defined by
g(z) = (e^(i*pi*(z/2))-1)/(e^(i*pi*(z/2))+1) and
h(z) = (e^(pi*(z/2))-1)/(e^(pi*(z/2))+1).
Let C represent the complex field. Show that g(z) maps...