Difference between revisions of "1999 AIME Problems/Problem 9"
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== Problem == | == Problem == | ||
| + | A function <math>\displaystyle f</math> is defined on the complex numbers by <math>\displaystyle f(z)=(a+bi)z,</math> where <math>\displaystyle a_{}</math> and <math>\displaystyle b_{}</math> are positive numbers. This function has the property that the image of each point in the complex plane is equidistant from that point and the origin. Given that <math>\displaystyle |a+bi|=8</math> and that <math>\displaystyle b^2=m/n,</math> where <math>\displaystyle m_{}</math> and <math>\displaystyle n_{}</math> are relatively prime positive integers. Find <math>\displaystyle m+n.</math> | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1999_AIME_Problems/Problem_8|Previous Problem]] | ||
| + | * [[1999_AIME_Problems/Problem_10|Next Problem]] | ||
* [[1999 AIME Problems]] | * [[1999 AIME Problems]] | ||
Revision as of 00:56, 22 January 2007
Problem
A function 
is defined on the complex numbers by 
where 
and 
are positive numbers. This function has the property that the image of each point in the complex plane is equidistant from that point and the origin. Given that 
and that 
where 
and 
are relatively prime positive integers. Find 
