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The Amplitude of 1 I is Equal to - Mathematics

MCQ

The amplitude of \[\frac{1}{i}\] is equal to

Options

  • 0

  • \[\frac{\pi}{2}\]

  • \[- \frac{\pi}{2}\]

  •  π

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Solution

\[- \frac{\pi}{2}\]

\[\text { Let } z = \frac{1}{i}\]

\[ \Rightarrow z=\frac{1}{i}\times\frac{i}{i}\]

\[ \Rightarrow z=\frac{i}{i^2}\]

\[ \Rightarrow z=-i\]

\[\text { Since } , z \left( 0, - 1 \right) \text { lies on the negative imaginary axis } . \]

\[\text { Therefore, } \arg (z) = \frac{- \pi}{2}\]

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Q 30 | Page 65
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