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2009 AIME I Problems/Problem 2

Revision as of 20:17, 19 March 2009 by Kubluck (talk | contribs) (New page: == Problem == There is a complex number <math>z</math> with imaginary part <math>164</math> and a positive integer <math>n</math> such that <cmath>\frac {z}{z + n} = 4i.</cmath> Find <m...)
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Problem

There is a complex number $z$ with imaginary part $164$ and a positive integer $n$ such that

\[\frac {z}{z + n} = 4i.\]

Find $n$.

Solution

Let $z$ = $a$ + $b$$i$

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