Q. 135.0( 2 Votes )

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

Answer :




= i


Let Z = i = r(cosθ + isinθ)


Now , separating real and complex part , we get


0 = rcosθ ……….eq.1


1 = rsinθ …………eq.2


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


1 = r2


Since r is always a positive no., therefore,


r = 1,


hence its modulus is 1.


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



tanθ =


Since cosθ = 0, sinθ = 1 and tanθ = . Therefore the θ lies in first quadrant.


tanθ = , therefore


Representing the complex no. in its polar form will be


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