2021 AMC 12A Problems/Problem 13
Problem
Of the following complex numbers 
, which one has the property that 
has the greatest real part?
Solution
Clearly 
and 
.
$\textbf{(B)} = 2\text{cis}(150)\$ (Error compiling LaTeX. Unknown error_msg)\textbf{(C)} =2\text{cis}(135)\$
$\textbf{(D)} =2\text{cis}(120)\$
Taking the real part of the 5th power of each we have$ (Error compiling LaTeX. Unknown error_msg)\textbf{(B):} 32\cos(650)=32\cos(30)=16\sqrt{3}$$ (Error compiling LaTeX. Unknown error_msg)\textbf{(C):} 32\cos(675)=32\cos(-45)=16\sqrt{2}$$ (Error compiling LaTeX. Unknown error_msg)\textbf{(D):} 32\cos(600)=32\cos(240)
\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. 
