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gotztahbeazn
Posts: 844
Location: Naperville, IL
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Posted: May 01, 2007, 5:31 pm •
# 1
 is a continuous complex-valued function satisfying:
i) 
ii) 
Find 
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"I want to die in my sleep, like my grandfather. Not like the passengers in his car." 
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t0rajir0u
Posts: 12301
Location: Cambridge, MA
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Posted: May 01, 2007, 6:23 pm •
# 2
Solution We know two things about : One, that it maps the unit circle to itself; another, that the origin,  , and  form an equilateral triangle. We conclude that must be a rotation by  in either direction; in other words, that  . Hence  .
Last edited by t0rajir0u on May 01, 2007, 7:02 pm, edited 3 times in total.
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gotztahbeazn
Posts: 844
Location: Naperville, IL
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Posted: May 01, 2007, 6:28 pm •
# 3
why does a rotation of  imply a third root of unity? wouldn't it be sixth root
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AstroPhys
Posts: 1027
Location: No Clue...Know Exactly How Fast Though
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Posted: May 01, 2007, 6:32 pm •
# 4
 It makes a triangle such that the angles are each .
Not a rotation though.
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t0rajir0u
Posts: 12301
Location: Cambridge, MA
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Posted: May 01, 2007, 7:03 pm •
# 5
gotztahbeazn wrote: why does a rotation of imply a third root of unity? wouldn't it be sixth root Sorry, you're right. I've fixed it. AstroPhys wrote: :maybe: It makes a triangle such that the angles are each . Not a rotation though. One leg of this triangle is , and the other is . Hence is a rotation of .
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Annoying Precision (http://qchu.wordpress.com/)
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nateharman1234
Posts: 278
Location: Chicago
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Posted: May 01, 2007, 7:20 pm •
# 7
I really dont think you should post this a day before it is due, do your own homework! And even if you are just posting this because you thought it was interesting, you should still wait until after it is due.
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gotztahbeazn
Posts: 844
Location: Naperville, IL
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Posted: May 01, 2007, 7:22 pm •
# 8
As far as I know the ARML coaches have always advocated kids working together and bouncing ideas off of each other.
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"I want to die in my sleep, like my grandfather. Not like the passengers in his car."
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nateharman1234
Posts: 278
Location: Chicago
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Posted: May 01, 2007, 7:27 pm •
# 9
I think they advocate working together and bouncing ideas of eachother, as in with other members of the team or with kids from your school, not over the internet, and especially not on a site where people post full solutions to problems posed.
but perhaps I am wrong.
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gotztahbeazn
Posts: 844
Location: Naperville, IL
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Posted: May 01, 2007, 7:32 pm •
# 10
heh it does you no good to post a question and copy the solution word for word and i agree that that would be cheating
however seeing as how i even corrected his solution, that shows that at least i understand his solution and i kno w where he's coming from with his solution and isn't that the point of hw?
anyways if the only reason you're posting this stuff is because you're worried that this might offset the proper team selection process, then take into account that the coaches consider your individual/power/relay performance during practice as well, in addition to AIME/AMC and ICTM stuff that you do
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"I want to die in my sleep, like my grandfather. Not like the passengers in his car."
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cincodemayo5590
Posts: 1143
Location: Chicago
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Posted: May 01, 2007, 7:32 pm •
# 11
Hey, kind of off topic, but I've completely lost my ARML schedule... the next practice is tomorrow? When are the others?
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Say this ten times quickly: The product of the sums of squares is greater than the square of the sum of products!
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gotztahbeazn
Posts: 844
Location: Naperville, IL
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Posted: May 01, 2007, 7:33 pm •
# 12
May 17th is the last one
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cincodemayo5590
Posts: 1143
Location: Chicago
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Posted: May 01, 2007, 7:33 pm •
# 13
gotztahbeazn wrote: May 17th is the last one
Ok, thanks. 
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Say this ten times quickly: The product of the sums of squares is greater than the square of the sum of products!
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Altheman
Posts: 6202
Location: Illinois
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Posted: May 01, 2007, 10:09 pm •
# 14
NOOOO THEY HAVE MADE POST RATINGS NOOOOO
anyway...i came up with and posted an almost identical problem before...so w/e
i.e. let g(x)=[1/x]f(x)
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