The principal value of the amplitude of (1 + i) is
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, $\arg (z)=\frac{\pi}{4}$