Difference between revisions of "2017 AMC 12A Problems/Problem 17"
(added problem and solution) |
|||
Line 12: | Line 12: | ||
This is real iff <math>\frac{n}{2}\in \mathbb{Z} \Leftrightarrow (n</math> is even<math>)</math>. Thus, the answer is the number of even <math>0\leq n<24</math> which is <math>\boxed{(D)=\ 12}</math>. | This is real iff <math>\frac{n}{2}\in \mathbb{Z} \Leftrightarrow (n</math> is even<math>)</math>. Thus, the answer is the number of even <math>0\leq n<24</math> which is <math>\boxed{(D)=\ 12}</math>. | ||
+ | |||
+ | == See Also == | ||
+ | {{AMC12 box|year=2017|ab=A|num-b=16|num-a=18}} |
Revision as of 15:18, 8 February 2017
Problem
There are different complex numbers such that . For how many of these is a real number?
Solution
Note that these such that are for integer . So
This is real iff is even. Thus, the answer is the number of even which is .
See Also
2017 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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 |