2012 AIME II Problems/Problem 8: Difference between revisions
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..." |
No edit summary |
||
| Line 2: | Line 2: | ||
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>. | ||
== Solution == | |||
== 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 
.
