一道复变函数不会,求把z=∞,0,1依次映射为w=0,2i,∞的分式线性映射

Question

一道复变函数不会,
求把z=∞,0,1依次映射为w=0,2i,∞的分式线性映射

Answer 1

f(z) = (az+b)/(cz+d)
f(∞) = 0 => a / c = 0 => a = 0
f(0) = 2i => b / d = 2i
f(1) = ∞ => 2i d / (c + d) = ∞ => c = -d
因此,f(z) = 2i / (1 - z)