If z = 1 - + i , then amp z= - Vidyadip

MCQ

If $z = 1 - \cos \alpha + i\sin \alpha $, then $amp \ z$=

A
$\frac{\alpha }{2}$
B
$ - \frac{\alpha }{2}$
C
$\frac{\pi }{2} + \frac{\alpha }{2}$
✓
$\frac{\pi }{2} - \frac{\alpha }{2}$

✓

Answer

Correct option: D.

$\frac{\pi }{2} - \frac{\alpha }{2}$

d
(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}$.

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