Question

Find the argument of the complex number z=1+iv3

Answer 1

Given:

The complex number is:

$z=1+i\sqrt{3}$

To find:

The argument of the given complex number.

Solution:

If a complex number is $z=x+iy$, then the argument of the complex number is:

$\theta=\tan^{-1}\dfrac{y}{x}$

We have,

$z=1+i\sqrt{3}$

Here, $x=1$ and $y=\sqrt{3}$. So, the argument of the given complex number is:

$\theta =\tan^{-1}\dfrac{\sqrt{3}}{1}$

$\theta =\tan^{-1}\sqrt{3}$

$\theta =\tan^{-1}\left(\tan \dfrac{\pi}{3}\right)$

$\theta =\dfrac{\pi}{3}$

Therefore, the argument of the given complex number is $\theta =\dfrac{\pi}{3}$.