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

= 4i - 4

Let Z = 4i - 4 = r(cosθ + isinθ)

Now , separating real and complex part , we get

-4 = rcosθ ……….eq.1

= 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,

tanθ = -√3

Since , and tanθ = -√3. therefore the θ lies in second quadrant.

Tanθ = -√3, therefore

Representing the complex no. in its polar form will be

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RS Aggarwal - Mathematics