Q. 104.7( 3 Votes )

Find the modulus of each of the following complex numbers and hence express each of them in polar form: 2 – 2i

Answer :

Let Z = 2 - 2i = r(cosθ + isinθ)


Now , separating real and complex part , we get


2 = rcosθ ……….eq.1


-2 = rsinθ …………eq.2


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


8 = r2


Since r is always a positive no. therefore,


r = 2,


hence its modulus is 2√2.


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



Tanθ = -1


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


Tanθ = -1, therefore


Representing the complex no. in its polar form will be


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