Difference between revisions of "2009 AIME I Problems/Problem 2"
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<cmath>\frac {z}{z+n}=4i</cmath> | <cmath>\frac {z}{z+n}=4i</cmath> |
Revision as of 12:03, 17 January 2016
Contents
Problem
There is a complex number with imaginary part and a positive integer such that
Find .
1st Solution
Let .
Then and
By comparing coefficients, equating the real terms on the leftmost and rightmost side of the equation,
we conclude that
By equating the imaginary terms on each side of the equation,
we conclude that
We now have an equation for :
and this equation shows that
2nd Solution
Since their imaginary 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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.