Let Z = -2 = r(cosθ + isinθ)

Now, separating real and complex part, we get

-2 = rcosθ………. eq.1

0 = 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,

Tanθ = 0

Since cosθ = -1, sinθ = 0 and tanθ = 0. Therefore the lies in second quadrant.

Tanθ = 0, therefore θ = π

Representing the complex no. in its polar form will be

Z = 2(cosπ + isinπ)