Q. 125.0( 1 Vote )

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

Answer :

Let Z = 3√2i - 3√2 = r(cos + isinθ)


Now, separating real and complex part , we get


-3√2 = rcosθ ……….eq.1


3√2 = rsinθ …………eq.2


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


36 = r2


Since r is always a positive no., therefore,


r = 6


hence its modulus is 6.


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




Since , and tanθ = -1 . therefore the θ lies in secothe nd quadrant.


Tanθ = -1 , therefore θ = .


Representing the complex no. in its polar form will be


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