Complex Numbers And Quadratic Equations question 215
Question: If $ {{( \frac{1+\cos \theta +i\sin \theta }{i+\sin \theta +i\cos \theta } )}^{4}}=\cos n\theta +i\sin n\theta $ , then $ n $ is equal to [EAMCET 1986]
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: D
Solution:
$ D^{r}=i(1+\cos \theta )+\sin \theta =2i{{\cos }^{2}}\frac{\theta }{2}+2\sin \frac{\theta }{2}\cos \frac{\theta }{2} $ \ L.H.S $ ={{[ \frac{\cos (\theta /2)+i\sin (\theta /2)}{i\cos (\theta /2)+\sin (\theta /2)} ]}^{4}} $ = $ \frac{1}{i^{4}}{{(\cos \theta +i\sin \theta )}^{4}}=\cos 4\theta +i\sin 4\theta $ .
BETA
