Question:
The principal value of the amplitude of (1 + i) is
(a) $\frac{\pi}{4}$
(b) $\frac{\pi}{12}$
(c) $\frac{3 \pi}{4}$
(d) $\pi$
Solution:
(a) $\frac{\pi}{4}$
Let $z=(1+i)$
$\tan \alpha=\left|\frac{\operatorname{Im}(z)}{\operatorname{Re}(z)}\right|$
= 1
$\Rightarrow \alpha=\frac{\pi}{4}$
Since, $z$ lies in the first quadrant.
Therefore, $\arg (z)=\frac{\pi}{4}$