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Question
The amplitude of \[\frac{1}{i}\] is equal to
Options
0
\[\frac{\pi}{2}\]
\[- \frac{\pi}{2}\]
π
Solution
\[- \frac{\pi}{2}\]
\[\text { Let } z = \frac{1}{i}\]
\[ \Rightarrow z=\frac{1}{i}\times\frac{i}{i}\]
\[ \Rightarrow z=\frac{i}{i^2}\]
\[ \Rightarrow z=-i\]
\[\text { Since } , z \left( 0, - 1 \right) \text { lies on the negative imaginary axis } . \]
\[\text { Therefore, } \arg (z) = \frac{- \pi}{2}\]
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