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(a) A basic building block is shown in Figure 1. Find the corresponding temperature and complex potential in the upper half-plane [10 points]. (b) What temperature in the first quadrant of the z-plane is obtained from (a) by the mapping w = a + z2 and what are the transformed boundary conditions [10 points]? (c) Find the temperature T* and the complex potential F* in the upper half-plane satisfying the boundary conditions in Figure 2 [10 points]. (d) Applying w = cosh (2) to (c), obtain the solution of the BVP in Figure 3 [10 points]. v V y T=0 TO T =T O CZ U T*=T u T*=0 ОО TET, T* = 0 T* = T. T=0 Figure 1 Figure 2 Figure 3