Let Z = -i = r(cosθ + isinθ)

Now , separating real and complex part , we get

0 = rcosθ……….eq.1

-1 = rsinθ …………eq.2

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

1 = r²

Since r is always a positive no., therefore,

r = 1,

hence its modulus is 1.

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

Tanθ = -∞

Since cosθ = 0 , sinθ = -1 and tanθ = -∞ . therefore the lies in fourth quadrant.

Tanθ = -∞, therefore

Representing the complex no. in its polar form will be