Find the bilinear transformation which maps the points z = 1, I, -1 onto w = 0,1,$\infty$

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written 7.9 years ago by

teamques10 ★ 65k

• modified 4.1 years ago

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written 7.9 years ago by

teamques10 ★ 65k

Let the transformation be $w = \frac{az + b}{cz + d}$

Now putting the value of z and w we get

1) w = 0, z = 1 0 = $\frac{a(1) + b}{c(1) + d} \therefore a+ b = 0$ i.e. a = -b

2) w = 1, z = …

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w = a(z-1)/ai(z+1) This step I don't understood

6.5 years ago by teamques10 ★ 65k

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