Complex Numbers And Quadratic Equations question 319
Question: If $ \omega $ is a complex number satisfying $ | \omega +\frac{1}{\omega } |=2 $ , then maximum distance of $ \omega $ from origin is
Options:
A) $ 2+\sqrt{3} $
B) $ 1+\sqrt{2} $
C) $ 1+\sqrt{3} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Since maximum distance of any complex number $ \omega $ from origin is given by $ |\omega | $ therefore, $ |\omega |=| \omega +\frac{1}{\omega }-\frac{1}{\omega } |\le | \omega +\frac{1}{\omega } |+| \frac{1}{\omega } |=2+\frac{1}{|\omega |} $
Þ $ |\omega {{|}^{2}}-2|\omega |-1\le 0 $
Þ $ |\omega |\le \frac{2\pm 2\sqrt{2}}{2} $ Hence max $ |\omega | $ is $ 1+\sqrt{2} $ .
BETA
