Difference between revisions of "2012 AIME II Problems/Problem 8"

(Created page with "== Problem 8 == The complex numbers <math>z</math> and <math>w</math> satisfy the system <cmath> z + \frac{20i}w = 5+i \\ \\ w+\frac{12i}z = -4+10i </cmath> Find the smallest pos...")
 
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The complex numbers <math>z</math> and <math>w</math> satisfy the system <cmath> z + \frac{20i}w = 5+i \\ \\
 
The complex numbers <math>z</math> and <math>w</math> satisfy the system <cmath> z + \frac{20i}w = 5+i \\ \\
 
w+\frac{12i}z = -4+10i </cmath> Find the smallest possible value of <math>\vert zw\vert^2</math>.
 
w+\frac{12i}z = -4+10i </cmath> Find the smallest possible value of <math>\vert zw\vert^2</math>.
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== Solution ==
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== See also ==
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{{AIME box|year=2012|n=II|num-b=7|num-a=9}}

Revision as of 17:21, 31 March 2012

Problem 8

The complex numbers $z$ and $w$ satisfy the system \[z + \frac{20i}w = 5+i \\ \\ w+\frac{12i}z = -4+10i\] Find the smallest possible value of $\vert zw\vert^2$.


Solution

See also

2012 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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