MCQ
The amplitude of $\frac{{1 + \sqrt 3 i}}{{\sqrt 3 + 1}}$ is
- ✓$\frac{\pi }{3}$
- B$ - \frac{\pi }{3}$
- C$\frac{\pi }{6}$
- D$ - \frac{\pi }{6}$
✓
Answer
Correct option: A.
$\frac{\pi }{3}$
a
(a)Let $z = \frac{{1 + i\sqrt 3 }}{{1 + \sqrt 3 }}\,\,\,\therefore amp(z)\,\,{\rm{or}}\,\,arg(z)$
$ = {\tan ^{ - 1}}\left[ {\frac{{\sqrt 3 /(1 + \sqrt 3 )}}{{1/(1 + \sqrt 3 )}}} \right] = {\tan ^{ - 1}}\sqrt 3 = \frac{\pi }{3}$
(a)Let $z = \frac{{1 + i\sqrt 3 }}{{1 + \sqrt 3 }}\,\,\,\therefore amp(z)\,\,{\rm{or}}\,\,arg(z)$
$ = {\tan ^{ - 1}}\left[ {\frac{{\sqrt 3 /(1 + \sqrt 3 )}}{{1/(1 + \sqrt 3 )}}} \right] = {\tan ^{ - 1}}\sqrt 3 = \frac{\pi }{3}$
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