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Leaky Nun
Leaky Nun
6:52 PM
f(z)=cos(h(z))
f'(z) = -sin(h(z)) h'(z)
f''(z) = -cos(h(z)) h'(z) - sin(h(z)) h''(z)
f(z) = cos(h(z)) = (exp(i h(z)) + exp(-i h(z)))/2
exp(ih)^2 - 2f exp(ih) + 1 = 0
exp(ih) = f +- sqrt(f^2 - 1))
= f +- sqrt(-g^2))
= f +- ig
aha
f^2 + g^2 = 1
(f+ig)(f-ig) = 1
f+ig is never 0, so there is h such that exp(h) = f+ig
exp(-h) = f-ig
etc
ok that was interesting
 

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