Complex Numbers And Quadratic Equations question 399
Question: If $ $ $ x+\frac{1}{x}=2\cos \theta , $ then x is equal to [RPET 2001]
Options:
A) $ \cos \theta +i\sin \theta $
B) $ \cos \theta -i\sin \theta $
C) $ \cos \theta \pm i\sin \theta $
D) $ \sin \theta \pm i\cos \theta $
Show Answer
Answer:
Correct Answer: C
Solution:
$ x+\frac{1}{x}=2\cos \theta $
$ \Rightarrow x^{2}-2x\cos \theta +1=0 $
Þ $ x=\frac{2\cos \theta \pm \sqrt{4{{\cos }^{2}}\theta -4}}{2} $
Þ $ x=\cos \theta \pm i\sin \theta $ .
BETA
