Alright all ive got the complex number
(8)^1/2 - i (24)^1/2.
So i put Tan theta = root 24 / root 8
I get theta as Pi/3.
Is this the principle agrument?
No it is not.
Note that if $\displaystyle x>0$ then $\displaystyle \arg(x+yi)=\arctan\left(\frac{y}{x}\right)$.
In this case $\displaystyle y=-\sqrt{24}$ so $\displaystyle \left(\frac{-\pi}{3}\right)$.