Difference between revisions of "2014 AIME I Problems/Problem 7"
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== Solution == | == Solution == | ||
| − | Let <math>w = \mathrm{cis}{\alpha}</math> and <math>z = 10*\mathrm{cis}{\beta}</math>. | + | Let <math>w = \mathrm{cis}{(\alpha)}</math> and <math>z = 10*\mathrm{cis}{(\beta)}</math>. |
== See also == | == See also == | ||
{{AIME box|year=2014|n=I|num-b=6|num-a=8}} | {{AIME box|year=2014|n=I|num-b=6|num-a=8}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 11:04, 15 March 2014
Problem 7
Let 
and 
be complex numbers such that 
and 
. Let 
. The maximum possible value of 
can be written as 
, where 
and 
are relatively prime positive integers. Find 
. (Note that 
, for 
, denotes the measure of the angle that the ray from 
to makes with the positive real axis in the complex plane.
Solution
Let 
and 
.
See also
| 2014 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
