I have been trying to solve the following question for a while now. I need to find the number of roots of:(adsbygoogle = window.adsbygoogle || []).push({});

f(z) = 6z^2 - 6 + Log(1+z)

in the area

D = { z is complex : |z-1| < 1 }

I assume this is solved by Rouche's theorem that requires me to find 2 analytic functions, h(z) and g(z) in D, where | g(z) | < | h(z) | on the verge of D, and f(z) = g(z) + h(z).

So I tried all possibilites, but none of them seem to work. Am I missing something?

Thanks.

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# Rouche's theorem

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