Find a Linear Fractional Transformation that maps points 0, i onto 0, 1, 0 in the angular region D-arg onto the unit disk w1.
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We know that a linear fractional transformation can be written as: f(z) = (az + b) / (cz + d) To map 0 to 0, we need f(0) = 0. Plugging in z = 0, we get: f(0) = (a(0) + b) / (c(0) + d) = b / d = 0 This implies that b = 0. To map i to 1, we need f(i) = 1. Show more…
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