Question: conformal mapping

I want to calculae the value of "Z" shape strip resistor like below. One end is AB and the other is FG,the thickness is t.
I want to use the Schwarz-Christoffel Mapping for this problem,"Z" shape to rectangle.
I have already find the map from rectangle to half plane,exp function.
But I can't find the analytic form relation from half plane to the "Z" shape.
Can you help me,please?
Thank you in advance.


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