2021 AMC 12B Problems/Problem 18: Difference between revisions
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Revision as of 19:37, 11 February 2021
Problem
Let 
be a complex number satisfying 
What is the value of 
Solution
Solution 1
The answer being in the form 
means that there are two solutions, some complex number and its complex conjugate. ![\[a+bi = \frac{6}{a-bi}\]](http://latex.artofproblemsolving.com/5/f/3/5f333ff36bfce8cc1cbef23b56cdc66c678671eb.png)
![\[a^2+b^2=6\]](http://latex.artofproblemsolving.com/a/0/0/a006fc3bc9d7d0863ef53f8dd41755cca1848ac8.png)
We should then be able to test out some ordered pairs of 
. After testing it out, we get the ordered pairs of 
and its conjugate 
. Plugging this into answer format gives us 
~Lopkiloinm
See Also
| 2021 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 17 |
Followed by Problem 19 |
| 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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