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Finding a conformal map to fit certain restrictions.

Find a conformal mapping which maps the upper half plane Im(z)>0 to |w|<1 such that w(a)=0 where a=a_x+ia_y and Im(a)=a_y>0.

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If w(a)=0, then we know this mapping will map its symmetric point a'=a_x-ia_y to w=infinity. So ...

Solution Summary

A conformal map is found.