2009 AIME I Problems/Problem 2
Problem
There is a complex number with imaginary part and a positive integer such that
Find .
Solution
1st Solution
Let .
Then and
From this, we conclude that and
We now have an equation for :
and this equation shows that
2nd solution
Since their imaginery part has to be equal,
See also
2009 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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All AIME Problems and Solutions |