Q. 95.0( 3 Votes )

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

Answer :

Let Z = - + 1 = r(cosθ + isinθ)


Now , separating real and complex part , we get


1 = rcosθ ……….eq.1


= rsinθ …………eq.2


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


4 = 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,




Since , and . therefore the θ lies in the fourth quadrant.


Tanθ = , therefore θ =


Representing the complex no. in its polar form will be


Z = 2{cos + isin}


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