Difference between revisions of "2002 AIME I Problems/Problem 12"
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== Problem == | == Problem == | ||
| − | Let <math>F(z)=\dfrac{z+1}{z-1}</math> for all | + | Let <math>F(z)=\dfrac{z+1}{z-1}</math> for all complex numbers <math>z\neq 1</math>, and let <math>z_n=F(z_{n-1})</math> for all positive integers <math>n</math>. Given that <math>z_0=\dfrac{1}{137}+i</math> and <math>z_{2002}=a+bi</math>, where <math>a</math> and <math>b</math> are real numbers, find <math>a+b</math>. |
== Solution == | == Solution == | ||
Revision as of 16:12, 25 September 2007
Problem
Let 
for all complex numbers 
, and let 
for all positive integers 
. Given that 
and 
, where 
and 
are real numbers, find 
.
Solution
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