Q. 115.0( 2 Votes )

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

Answer :

Let Z = 4√2i - 4 = r(cosθ + isinθ)


Now, separating real and complex part , we get


-4 = rcosθ ……….eq.1


4√3 = rsinθ …………eq.2


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


64 = r2


Since r is always a positive no., therefore,


r = 8


hence its modulus is 8.


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




Since , and . therefore the lies in second the quadrant.


Tanθ = -√3, therefore θ= .


Representing the complex no. in its polar form will be


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