Friday, February 22, 2013

Suppose that f is holomorphic on C and that the real part of f is positive for all z. Show that f is constant?

I assume that you need to show that f is bounded, to use Liouville's Theorem. But I don't see how being bounded below on the real part makes the whole function bounded. I also haven't yet learnt about lattices and/or poles, so should be able to answer the question without using them. Any ideas would be really helpful. Thanks.

What is a VPN?


VPN is (Virtual Private Network) were first used by companies to enable their employees to securely access internal systems such as email remotely (e.g. from home or while on business trips). Today they are increasingly being used for personal use by individuals to protect their privacy while online in public places (e.g. when using the wi-fi connection in a cafe) or in a country where the internet is censored / blocked (e.g. China, Saudi Arabia…).

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