Letbe differentiable, withf:C→Cfor allf(z)/=0 (not equal)inzSupposeC.limz→z0exist and is nonzero. Prove that f is constant.f(z)

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- May 7th 2011, 12:19 PMAcCeylanto prove f is constant
Let

be differentiable, with**f:C→C**for all**f(z)/=0 (not equal)**in*z*Suppose**C.****limz→z0**exist and is nonzero. Prove that f is constant.**f(z)** - May 7th 2011, 12:25 PMTheEmptySet
- May 7th 2011, 12:37 PMAcCeylan
Yes you are true!!?? but I found this question in a complex analysis book, I tried to solve but I hadnt thought that it could be false..!!

- May 8th 2011, 09:22 AMTinyboss
Can you get that f is an entire function whose image misses a neighborhood of zero? In that case, 1/f is a bounded entire function, and you can apply Liouville's.

- May 14th 2011, 04:59 AMAcCeylan
Take limit e^z as z→-infinity it equal to zero, so it not satisfy the statement. I proved this statement with using Liouville Theorem