Difference between revisions of "1985 AHSME Problems/Problem 23"
(Created page with "==Problem== If <math> x=\frac{-1+i\sqrt{3}}{2} </math> and <math> y=\frac{-1-i\sqrt{3}}{2} </math>, where <math> i^2=-1 </math>, then which of the following is ''not'' correct? ...") |
|||
Line 48: | Line 48: | ||
==See Also== | ==See Also== | ||
{{AHSME box|year=1985|num-b=22|num-a=24}} | {{AHSME box|year=1985|num-b=22|num-a=24}} | ||
+ | {{MAA Notice}} |
Revision as of 13:01, 5 July 2013
Problem
If and
, where
, then which of the following is not correct?
Solution
Notice that and
. We have
.
We also have .
Finally,
.
Let . We have
.
For , so
.
Therefore, for , and
, so
.
As a check, we have for
, and
.
Finally, for we have
, and
, and this is true for all other answer choices.
See Also
1985 AHSME (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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.