If \(P\) is the point in the Agrand diagram corresponding to the complex number \(\sqrt{3}+i\) and if \(O P Q\) is an isosceles right angled triangle, right angled at ' \(O\) ', then \(Q\) represents the complex number

Let \(z=\sqrt{3}+i\)



\(
\begin{aligned}
\therefore \quad \arg (\mathrm{z}) &=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right) \\
&=30^{\circ}
\end{aligned}
\)
For making a right angled triangle OPQ, point \(Q\) either in IInd quadrant or IVth quadrant.
If the point \(Q\) is in Ind quadrant, then we take \(\theta=120^{\circ}\)
\(
\begin{aligned}
\therefore \quad \tan 120^{\circ} &=-\cot 30^{\circ} \\
&=\frac{\sqrt{3}}{-1}
\end{aligned}
\)
\(\therefore\) Point \(Q\) is \((-1, \sqrt{3})\) and if the point \(Q\) is in IVth quadrant, then we take
\(
\begin{aligned}
\theta &=-60^{\circ} \\
\therefore \quad \tan \left(-60^{\circ}\right) &=-\tan 60^{\circ} \\
&=-\frac{1}{\sqrt{3}}
\end{aligned}
\)
\(\therefore\) Point \(\mathrm{Q}\) is \((1,-\sqrt{3})\).
Hence, option (a) is correct.