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` .**

Shall I edit the question like this?

**Find the argument(1-i) or in short form arg(1-i)**:

1-i is a complex number, which can be written in polar coordinates, explaied below.

The complex number, z is written in the form :

z = x+iy, where x is the real part and y is the imaginary part of the complex number .

We nomalise the complex number and write it as below in order to express its real and imaginary parts as cosine of an angle **a ** and sine of an angle **a** times the **modulus** of the complex number to conver it into polar form:

z = sqrt(x^2+y^2){x/sqrt(x^2+y^2) +i* y/sqrt(x^2+y^2)}

=r(cos a + i*sin a), where r=sqrt(x^2+y^2) and sina =x/r

cosa = y/r

**Then, tan a = x/y. or**

** arg(z) =a = arctg(x/y)**.

In the given problem:

Let z = 1- i = sqrt(2){ 1/sqrt2+i(-1/sqrt2)}

x=1 and y=-1.

**arg(z) **= **arg(1 -i**) = ** arctg [(-1/(+1)] **= (-pi/4) = **-pi/4 **= **-45 degree.**

Hope this helps you.