Difference between revisions of "2002 AIME I Problems/Problem 12"
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== Problem == | == Problem == | ||
| − | Let <math>F(z)=\dfrac{z+ | + | Let <math>F(z)=\dfrac{z+i}{z-i}</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 09:58, 6 February 2008
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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See also
| 2002 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
