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Question
The principal value of the amplitude of (1 + i) is
Options
\[\frac{\pi}{4}\]
\[\frac{\pi}{12}\]
\[\frac{3\pi}{4}\]
π
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Solution
\[\frac{\pi}{4}\]
Let z = (1+i)
\[\tan \alpha = \left| \frac{\text { Im }(z)}{Re(z)} \right|\]
\[ = 1\]
\[ \Rightarrow \alpha = \frac{\pi}{4}\]
\[\text { Since, z lies in the first quadrant }. \]
Therefore, arg (z) =\[\frac{\pi}{4}\]
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