- Home
- Standard 11
- Mathematics
4-1.Complex numbers
easy
If $z = 1 - \cos \alpha + i\sin \alpha $, then $amp \ z$=
A
$\frac{\alpha }{2}$
B
$ - \frac{\alpha }{2}$
C
$\frac{\pi }{2} + \frac{\alpha }{2}$
D
$\frac{\pi }{2} - \frac{\alpha }{2}$
Solution
(d) $amp(z) = {\tan ^{ – 1}}\frac{{\sin \alpha }}{{1 – \cos \alpha }}$
$ = {\tan ^{ – 1}}\left( {\cot \frac{\alpha }{2}} \right) = {\tan ^{ – 1}}\left\{ {\tan \left( {\frac{\pi }{2} – \frac{\alpha }{2}} \right)} \right\} = \frac{\pi }{2} – \frac{\alpha }{2}$.
Standard 11
Mathematics
