The principal value of the argument of the complex number

Since $z=1-i=1+i(-1)$

here $\theta=\tan ^{-1}\left|\frac{-1}{1}\right|$

$\theta=\tan ^{-1} 1=\frac{\pi}{y}$

Since z lies in 4th quadrant.

$\therefore$ argument is given by $\frac{-\pi}{y}$