Q. 165.0( 3 Votes )

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

Answer :




= -i - 1


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,


r = √2,


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 third quadrant.


Tanθ = 1, therefore


Representing the complex no. in its polar form will be


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