2023 AMC 12B Problems/Problem 12
Revision as of 17:00, 15 November 2023 by Failure.net (talk | contribs)
Problem
For complex number and
(where
), define the binary operation
Suppose is a complex number such that
. What is
?
Solution 1
let =
.
.
This is equal to
Since the real values have to be equal to each other,
Simple algebra shows
, so
is
.
The imaginary components must also equal each other, meaning
, or
. This means
.
Thus, the magnitude of z is
~zhenghua
~Failure.net