Difference between revisions of "2021 AMC 12A Problems/Problem 13"
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==Solution== | ==Solution== | ||
First, <math>\textbf{(B)} = 2\text{cis}(150), \textbf{(C)} =2\text{cis}(135)</math><math>, \textbf{(D)} =2\text{cis}(120)</math>. | First, <math>\textbf{(B)} = 2\text{cis}(150), \textbf{(C)} =2\text{cis}(135)</math><math>, \textbf{(D)} =2\text{cis}(120)</math>. | ||
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Taking the real part of the 5th power of each we have: | Taking the real part of the 5th power of each we have: | ||
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<math>\textbf{(A):} (-2)^5=-32</math>, | <math>\textbf{(A):} (-2)^5=-32</math>, | ||
<math>\textbf{(B):} 32\cos(650)=32\cos(30)=16\sqrt{3}</math>, | <math>\textbf{(B):} 32\cos(650)=32\cos(30)=16\sqrt{3}</math>, | ||
Revision as of 15:45, 11 February 2021
Problem
Of the following complex numbers 
, which one has the property that 
has the greatest real part?
Solution
First, 
.
Taking the real part of the 5th power of each we have:
,
,
,
which is negative, and
\boxed{\textbf{(B)}}$.
~JHawk0224
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 12 |
Followed by Problem 14 |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
