Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1972 AHSME Problems/Problem 3"

(→‎Solution)
(→‎Solution)
 
Line 11: Line 11:
 
== Solution ==
 
== Solution ==
  
−
Using DeMoivre's theorem, we can calculate <math>x^2=\frac{1+i\sqrt{3}}{2}</math> The denominator is therefore <math>-1</math> which makes the answer <cmath>\boxed{\textbf{(C) }-1.</cmath> ~lopkiloinm
+
Using DeMoivre's theorem, we can calculate <math>x^2=\frac{1+i\sqrt{3}}{2}</math> The denominator is therefore <math>-1</math> which makes the answer <cmath>\boxed{\textbf{(C) }-1}.</cmath> ~lopkiloinm

Latest revision as of 00:54, 7 November 2020

Problem 3

If $x=\dfrac{1-i\sqrt{3}}{2}$ where $i=\sqrt{-1}$, then $\dfrac{1}{x^2-x}$ is equal to

$\textbf{(A) }-2\qquad \textbf{(B) }-1\qquad \textbf{(C) }1+i\sqrt{3}\qquad \textbf{(D) }1\qquad \textbf{(E) }2$

Solution

Using DeMoivre's theorem, we can calculate $x^2=\frac{1+i\sqrt{3}}{2}$ The denominator is therefore $-1$ which makes the answer \[\boxed{\textbf{(C) }-1}.\] ~lopkiloinm

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1972_AHSME_Problems/Problem_3&oldid=136868"