Difference between revisions of "2020 AMC 12B Problems/Problem 23"
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| + | ==Problem 23== | ||
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| + | How many integers <math>n \geq 2</math> are there such that whenever <math>z_1, z_2, ..., z_n</math> are complex numbers such that | ||
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| + | <cmath>|z_1| = |z_2| = ... = |z_n| = 1 \text{ and } z_1 + z_2 + ... + z_n = 0,</cmath> | ||
| + | then the numbers <math>z_1, z_2, ..., z_n</math> are equally spaced on the unit circle in the complex plane? | ||
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| + | <math>\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 5</math> | ||
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| + | [[2020 AMC 12B Problems/Problem 23|Solution]] | ||
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| + | ==Solution== | ||
==See Also== | ==See Also== | ||
Revision as of 23:54, 7 February 2020
Problem 23
How many integers 
are there such that whenever 
are complex numbers such that
![\[|z_1| = |z_2| = ... = |z_n| = 1 \text{ and } z_1 + z_2 + ... + z_n = 0,\]](http://latex.artofproblemsolving.com/3/b/5/3b5ec1e5f9204ea20f9438cf2c48b0c9464f27ac.png)
then the numbers are equally spaced on the unit circle in the complex plane?
Solution
See Also
| 2020 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 22 |
Followed by Problem 24 |
| 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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