Question

The argument of the complex number $ \left( \frac{i}{2}-\frac{2}{i} \right) $ is equal to

• A. $ \frac{\pi }{4} $
• B. $ \frac{3\pi }{4} $
• C. $ \frac{\pi }{12} $
• D. $ \frac{\pi }{2} $

Answer 1

The Correct Option is D

Let $ z=\frac{i}{2}-\frac{2}{i}=\frac{i}{2}-\frac{2i}{{{i}^{2}}} $ $ Z=\frac{i}{2}+2i=\frac{5}{2}i=0+\frac{5}{2}i $ $ \arg (z)={{\tan }^{-1}}\left( \frac{\operatorname{Im}(z)}{\operatorname{Re}(z)} \right) $
$={{\tan }^{-1}}\left( \frac{5/2}{0} \right)={{\tan }^{-1}}(\infty ) $
$={{\tan }^{-1}}\left( \tan \frac{\pi }{2} \right)=\frac{\pi }{2} $