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Science Forum Index » Math - Numerical Analysis Forum » sum of real and imaginary parts constant?
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| Guest |
 Posted: Mon Dec 18, 2006 3:49 am |
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Hey, my flat-mates left this problem on the fridge, and its driving me
nuts! (game we play...)
Let f be an entire function such that Re(f(z))+Im(f(z)) < 1 for all z.
Show that f is constant.
So far, I've got that f is holomorphic and entire...
Thanks for any help! |
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| Robert Israel |
| Posted: Mon Dec 18, 2006 3:51 pm |
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Guest
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In article <1166428150.098160.284810@79g2000cws.googlegroups.com>,
<bensaou@gmail.com> wrote:
Quote: Hey, my flat-mates left this problem on the fridge, and its driving me
nuts! (game we play...)
Let f be an entire function such that Re(f(z))+Im(f(z)) < 1 for all z.
Show that f is constant.
So far, I've got that f is holomorphic and entire...
Thanks for any help!
Hint: Apply a fractional linear transformation and then use
Liouville's Theorem.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada |
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