2023 AMC 12B Problems/Problem 12
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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
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