Q. 34.0( 3 Votes )

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

Answer :

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 lies in fourth quadrant.


Tanθ = -, therefore


Representing the complex no. in its polar form will be



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