Find the modulus of each of the following complex numbers and hence express each of them in polar form: 2i

Let Z = 2i = r(cosθ + isinθ)

Now , separating real and complex part , we get

0 = rcosθ ……….eq.1

2 = 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 = ∞

Since cosθ = 0, sinθ = 1 and tanθ = ∞. Therefore the θ lies in first quadrant.

tanθ = ∞, therefore

Representing the complex no. in its polar form will be