To find the argument of the complex number 1-i you need to transform the given rectangular form into the polar form.

You need to remember how to transform the rectangular form of a complex number z = x+iy into the polar form`z = (sqrt(x^2+y^2))*(cos theta + isin theta).`

`theta` denotes the argument...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

To find the argument of the complex number 1-i you need to transform the given rectangular form into the polar form.

You need to remember how to transform the rectangular form of a complex number z = x+iy into the polar form`z = (sqrt(x^2+y^2))*(cos theta + isin theta).`

`theta` denotes the argument of the complex number.

`theta = arctan (y/x)`

Comparing the standard form of a comples number with the given complex number yields: x = 1; y = -1

`theta = arctan(-1/1) = arctan (-1) = -pi/4`

`sqrt(x^2+y^2) = sqrt(1+1) = sqrt2`

The polar form of the given complex number is `z=sqrt2*(cos(pi/4) - i*sin(pi/4)).`

**The argument of the given complex number is `theta = -pi/4` .**