2023 AMC 12B Problems/Problem 12
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Contents
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
~Failure.net
Video Solution
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
See Also
2023 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 11 |
Followed by Problem 13 |
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 | |
All AMC 12 Problems and Solutions |
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