2004 AMC 12B Problems/Problem 16
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 • Answer Key • Resources) | |
Preceded by Problem 15 |
Followed by Problem 17 |
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All AMC 12 Problems and Solutions |