Question

How do you find an argument?

Answer 1

The argument of Complex Numbers Definition :

The argument of a complex number is defined as the angle inclined from the real axis in the direction of the complex number represented on the complex plane.

It is denoted by $“\theta ”$or $“\phi ”$. It is measured in the standard unit called “radians”.

The argument of Complex Numbers Formula :

In polar form, a complex number is represented by the equation $r(\cos \theta +i\sin \theta )$ here, $\theta$is the argument.

The argument function is denoted by $arg\left(z\right)$, where $z$ denotes the complex number, that is $z=x+iy$.

The computation of the complex argument can be done by using the following formula:

$\begin{array}{rcl}\mathbf{a}\mathbf{r}\mathbf{g}\mathbf{}\mathbf{\left(}\mathbf{z}\mathbf{\right)}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{a}\mathbf{r}\mathbf{g}\mathbf{}\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{i}\mathbf{y}\mathbf{)}\mathbf{}\\ & =& {\tan }^{-1}\left(\frac{y}{x}\right)\end{array}$

Therefore, the argument $\theta$is represented as:

$\theta ={\tan }^{-1}\left(\frac{y}{x}\right)$

Hence, In this way we can calculate an argument of a complex number.