Answer :

Let √3 = r cos θ and 1 = r sin θ ……….(i)


Squaring both sides, we get


3= r2 cos2 θ and 1 = r2 sin2 θ


Adding both the equations, we get


3 + 1 = r2 cos2 θ + r2 sin2 θ


4 = r2 (cos2 θ + sin2 θ)


4 = r2 or r2 = 4 [ sin2 θ + cos2 θ = 1]


r = √4


r = 2 (conventionally, r>0)


Substituting r = 2 in (i), we get


√3 = 2 cos θ and 1 = 2 sin θ




We know that the complex number √3 + i lies in the first quadrant and the value of the argument lies between - π and π, i.e. - π < θ ≤ π.




As we know that the polar representation of a complex number z = x + iy is


z = r (cos θ + i sin θ) where is the modulus of the complex number and θ is the argument of the complex number, denoted by arg z.


So, the required polar form is .


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