Consider a Mobius transformation Determine the constants a, b, c, and d, (all ), such that the transformation maps 0 i, −i 1, and −1 0. How would I work this out?
Last edited by ronaldo_07; Jan 21st 2009 at 09:56 PM.
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What's mapped to ? Looks like you forgot to type it.
Originally Posted by chiph588@ What's mapped to ? Looks like you forgot to type it. sorry 0 is mapped to i
Originally Posted by ronaldo_07 Consider a Mobius transformation Determine the constants a, b, c, and d, (all ), such that the transformation maps 0 i, −i 1, and −1 0. How would I work this out? The way to do this is to cross products equal to each other. Solving for , we get
Setting the cross products equal, I get (z-(-i))/z-(-1) x 0-(-1)/0-(-i) = (w-1)/(w-0) x (i-0)/(i-1) (z+i)/(iz+i) = (iw-i)/(iw-w) and getting w by itself w = (z+1)/(iz-i) a = 1, b = 1, c = i, d = -i
Multiply numerator and denominator by and you'll get my answer.
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