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CTK Exchange
ugur
guest
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May-01-09, 07:58 PM (EST) |
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"complex numbers"
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Hello, i want to ask something about the lemma on this page. https://www.cut-the-knot.org/fta/vaggione.shtmlhere, b is a complex number and a sequence in complex is taken to be such that b(z_n - a )^k is negative real number, where k is a natural number greater than equal to 1. if k of the form 4n+1,4n+2,4n+3 its ok. a sequence can easily be found. but what if 4n? i couldnt figure it out. i appreciate all help. thank you. |
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alexb
Charter Member
2367 posts |
May-01-09, 08:36 PM (EST) |
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1. "RE: complex numbers"
In response to message #0
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>Hello, i want to ask something about the lemma on this page. >https://www.cut-the-knot.org/fta/vaggione.shtml > >here, b is a complex number and a sequence in complex is >taken to be such that b(z_n - a )^k is negative real number, >where k is a natural number greater than equal to 1. > >if k of the form 4n+1,4n+2,4n+3 its ok. a sequence can >easily be found. but what if 4n? i couldnt figure it out. i >appreciate all help. >Let bk be one of the kth roots of b: (bk)k = b. Let wn,k be one of kth roots of -1/n and set zn = wn,k / bk + a. (Certainly zn -> a as n goes to infinity.) For this zn, b(zn - a)k = -1/n < 0.
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