Complex Numbers And Quadratic Equations question 104
Question: If $ z=1-\cos \alpha +i\sin \alpha $ , then amp $ z $ =
Options:
A) $ \frac{\alpha }{2} $
B) $ -\frac{\alpha }{2} $
C) $ \frac{\pi }{2}+\frac{\alpha }{2} $
D) $ \frac{\pi }{2}-\frac{\alpha }{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
amp $ (z)={{\tan }^{-1}}\frac{\sin \alpha }{1-\cos \alpha } $ $ ={{\tan }^{-1}}( \cot \frac{\alpha }{2} )={{\tan }^{-1}}{ \tan ( \frac{\pi }{2}-\frac{\alpha }{2} ) }=\frac{\pi }{2}-\frac{\alpha }{2} $ .
BETA
