The argument of the complex number   \(\sqrt { - 1} \) is

Concept:

The argument of z is the angle between the positive real axis and the line joining the point to the origin.

if a complex function is given by, z = x +iy, then the argument of z = arg(z) = \({\tan ^{ - 1}}\left( {\frac{y}{x}} \right)\)

 Calculations: 

Given, the complex number \(\sqrt { - 1} \)

⇒ \(z = \sqrt { - 1} = i\) = x + iy

By comparing,

⇒ x = 0 and y = 1

⇒ z lies in the first quadrant.

Hence, arg(z) = \( tan^{-1}( \frac{y}{x})\)

⇒arg(z) = \( tan^{-1} (\frac{1}{0})\;=\;\frac{{\pi}}{{2}}\)

⇒ arg(z) = \( \frac{\pi}{2}\) 

Hence, the argument of the complex number  \(z = \sqrt { - 1} = i\) is \(\frac{\pi}{2}\)