2004 AMC 12B Problems/Problem 16
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Problem
A function 
is defined by 
, where 
and 
is the complex conjugate of 
. How many values of satisfy both 
and 
?
Solution
Let 
, so 
. By definition, 
, which implies that all solutions to lie on the line 
on the complex plane. The graph of is a circle centered at the origin, and there are 
intersections.
See also
| 2004 AMC 12B (Problems • Resources) | ||
| Preceded by Problem 15 | Followed by Problem 17 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
