Difference between revisions of "2012 AIME II Problems/Problem 8"
Williamhu888 (talk | contribs) (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 == | ||
| + | {{AIME box|year=2012|n=II|num-b=7|num-a=9}} | ||
and 
satisfy the system ![\[z + \frac{20i}w = 5+i \\ \\ w+\frac{12i}z = -4+10i\]](http://latex.artofproblemsolving.com/a/8/8/a8862654235e060c0fc69dd97636c08c0755403e.png)
Find the smallest possible value of 
.
