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?
Tricky application of Rouché's Theorem
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complex-analysis
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3Once will be enough. Hint: show $|9 z e^{z+1}| > |z^{10} - 8|$ on the unit circle. – 2011-08-07
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0Thx a lot, I got it! – 2011-08-07
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0@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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0Or 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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0Ok, I'll answer the question. – 2011-08-07