Question

The principal value of the argument of

(1+i√3)(1−i) is____

Answer 1

$$(1+3i)(1-i)=1-i+3i+3=4+2i$$

$$x=4>0, y=2$$

$$\text{Arg}(4+2i)=\tan^{-1}\big(\dfrac{2}{4}\big)$$

$\text{Arg}((1+3i)(1-i))$ is $\tan^{-1}\big(\dfrac{1}{2}\big).$