2020 AMC 12B Problems/Problem 23
Problem 23
How many integers are there such that whenever are complex numbers such that
then the numbers are equally spaced on the unit circle in the complex plane?
Solution
For , we see that if , then , so they are evenly spaced along the unit circle.
For , WLOG, we can set . Notice that now and $Im\{z_{1}\}=-\IM\{z_{2}\}$ (Error compiling LaTeX. Unknown error_msg)
See Also
2020 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 22 |
Followed by Problem 24 |
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