Answer :

Let Z = 1 - i = r(cosθ + isinθ)


Now , separating real and complex part , we get


-1 = rcosθ ……….eq.1


1 = rsinθ …………eq.2


Squaring and adding eq.1 and eq.2, we get


2 = r2


Since r is always a positive no., therefore,


,


hence its modulus is √2.


now, dividing eq.2 by eq.1 , we get,



Tanθ = -1


Since and tanθ = -1. therefore the θ lies in second quadrant.


Tanθ = -1, therefore


Representing the complex no. in its polar form will be


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