Find the modulus

Let Z = - - √3 = r(cosθ + isinθ)

Now , separating real and complex part , we get

-√3 = rcosθ ……….eq.1

-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 third quadrant.

, therefore .

Representing the complex no. in its polar form will be

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