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    Hi there!

    Could you help me find out the number of zeros of the this function in D(0;1)

    Cos \pi z-100z^{100}

    where z is complex.

    Thank you as I'm rather stuck here.
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    I don't know how much use it is to you. I also don't understand D(0;1) but you could try turning 100z^{100} into the modulus argument form.
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    (Original post by Goldenratio)
    Hi there!

    Could you help me find out the number of zeros of the this function in D(0;1)

    Cos \pi z-100z^{100}

    where z is complex.
    Do you know Rouche's theorem?

    [Meta-comment: It's fairly obvious to me from your posts over the last few days that you're doing some kind of complex analysis course, and so the questions you're asking are typically applications of some topic just covered in the course. Unfortunately, I don't remember Complex Variable well enough to immediately spot the topic. So in future, if you could say "we've just done the argument principle", etc., when you ask the question, I could make a better guess at how you're supposed to approach it].

    @Insparato: D(0,1) is the unit disc (centre 0, radius 1). I don't think you can do this question without a university level knowledge of complex analysis though.
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    Thank you! I had in mind Rouché's Theorem which states that if f and g are analytic in and on a closed contour D, then if |f|>|g| hence f+g have the same number of zeros as f. But the reason i had not mentioned any particular theorem was that I was hoping you would come with an open mind and might see some way of solving it which did not use this theorem. That's what I like about TSR in particular
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    ha! I know nothing about complex analysis except rouche's theorem, and I was thinking about suggesting it. what a coincidence, I guess complex analysis is a small subject
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    (Original post by Goldenratio)
    Thank you! I had in mind Rouché's Theorem which states that if f and g are analytic in and on a closed contour D, then if |f|>|g| hence f+g have the same number of zeros as f. But the reason i had not mentioned any particular theorem was that I was hoping you would come with an open mind and might see some way of solving it which did not use this theorem. That's what I like about TSR in particular
    Yeah, but it's been 20 years since I did Complex Analysis and I'm not current on it. It was a real 'tip-of-my-tongue' moment to remember the word Rouche to google on, and even then my recollection of what it said was a bit off.

    So I think you're better off giving the hint.

    (Also, in some cases, there may be 2 or more different ways of doing something. I know you say you want people to have an open mind, but the lecturer sets questions to give you practice in the topics they're teaching, so if we come up with some completely different method, it means you're actually missing the point the lecturer was trying to make. There's been at least one question you've asked previously where I think this has happened (the integral some people did with a t/2 substitution)).
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    I didn't expect to be of much help, albeit i had a quick google of zeroes of a function and thought there must've been something im not getting.
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    (Original post by DFranklin)
    (Also, in some cases, there may be 2 or more different ways of doing something. I know you say you want people to have an open mind, but the lecturer sets questions to give you practice in the topics they're teaching, so if we come up with some completely different method, it means you're actually missing the point the lecturer was trying to make. There's been at least one question you've asked previously where I think this has happened (the integral some people did with a t/2 substitution)).
    hmm I like to learn both methods. But you're right in what you say if I was not first using the method I was given by the lecturer.
 
 
 
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