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(a) Find Mbius transforms that permute 0, 1, in all possible ways. That is, nd Mbius transforms f1 through f6 so that f1 (0) = 0 f1 (1) = 1 f1 () =…

(a) Find Mbius transforms that permute 0, 1, in all possible ways. That is, nd Mbius transforms f1 through f6 so that f1 (0) = 0 f1 (1) = 1 f1 () =…

(a) Find Mbius transforms that permute 0, 1, 1 in all possible ways. Thatis, nd Mbius transforms f1 through f6 so thatf1(0) = 0 f1(1) = 1 f1(1) = 1f2(0) = 0 f2(1) = 1 f2(1) = 1f3(0) = 1 f3(1) = 0 f3(1) = 1f4(0) = 1 f4(1) = 0 f4(1) = 1f5(0) = 1 f5(1) = 1 f5(1) = 0f6(0) = 1 f6(1) = 1 f6(1) = 0:(You should be able to see patterns and use tricks; you don’t need tocompute six independent functions.)(b) Next we will try to understand as well as we can what one of these func-tions does. Find and plot what f4 does to the 6 poles of the sphere0; 1; i;????1;????i;1. Indicate where the natural circles through these 6points go. That is, indicate what happens to the real axis, the imag-inary axis, and the unit circle.(c) There are two xed points of f4; nd and plot them.(d) The real axis, the imaginary axis, and the unit circle divide the planeinto 8 regions. Indicate where each of these regions get mapped to.

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