Suppose that f is analytic on a domain D, which contains a simple closed curve lambda and the inside of lambda. If |f| is constant on lambda, then either f is constant or f has a zero inside lambda ...(adsbygoogle = window.adsbygoogle || []).push({});

i am supposed to use maximum/modulus principle to prove it ...

here is my take:

if f is constant, i dont see a reason why |f| wouldnt be constant :)

if f is not constant, then the max/min principle applies ...

meaning |f| can not have any local max/min on D

now i am lost at this point ...

i would also like a little clarification on what f is constant on lambda means, because the way i see it .. .if lambda is a closed loop (say a circle), then how can f be always increasing /decreasing ...? maybe i am misinterpreting the problem

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# Complex analysis - maximum/modulus principle

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