Difference between revisions of "2009 AIME I Problems/Problem 2"
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<cmath>\frac {1}{1-4i}=\frac {z+n}{n}</cmath> | <cmath>\frac {1}{1-4i}=\frac {z+n}{n}</cmath> | ||
− | <cmath>\frac {1+4i}{17}=\frac {z}{n} | + | <cmath>\frac {1+4i}{17}=\frac {z}{n}+1</cmath> |
Since their imaginery part has to be equal, | Since their imaginery part has to be equal, |
Revision as of 22:33, 19 March 2009
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |