= i

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 θ lies in first quadrant.

tanθ = ∞, therefore

Representing the complex no. in its polar form will be

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