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

= √3i + 1

Let Z = √3i + 1 = r(cosθ + isinθ)

Now , separating real and complex part , we get

1 = rcosθ ……….eq.1

√3 = 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 = √3

Since , and tanθ = . therefore the θ lies in first quadrant.

Tanθ = √3, therefore

Representing the complex no. in its polar form will be

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