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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` .

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