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I want to find how many zero's does $z^{10} + 9ze^{z+1}-8$ have in the open unit disc. Do I need to apply Rouché's Theorem twice?

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    Once will be enough. Hint: show $|9 z e^{z+1}| > |z^{10} - 8|$ on the unit circle.2011-08-07
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    Thx a lot, I got it!2011-08-07
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    @robert: It would be nice if you make that comment, into an answer so that this question doesn't remain in the unanswered list.2011-08-07
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    Or perhaps, the OP can can answer the question himself, since now he has got the idea for solving the problem.2011-08-07
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    Ok, I'll answer the question.2011-08-07

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