Question

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

Answer 1

Given:

The complex number is:

`z=1+i√(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)(y)/(x)`

We have,

`z=1+i√(3)`

Here,
`x=1` and
`y=√(3)`. So, the argument of the given complex number is:

`\theta =\tan^(-1)(√(3))/(1)`

`\theta =\tan^(-1)√(3)`

`\theta =\tan^(-1)\left(\tan (\pi)/(3)\right)`

`\theta =(\pi)/(3)`

Therefore, the argument of the given complex number is
`\theta =(\pi)/(3)`.