Represent the complex number z = 1 + i√3 in the polar form.

Complex Analysis Questions

Complex Analysis

Q.Represent the complex number z = 1 + i√3 in the polar form.

Sol.

1 + i√3 = r(cos θ + isinθ)

∴ rcosθ = 1 ...(1)

and rsinθ = √3 ...(2)

Squring and adding (1) and (2), we get,

r2(cos2θ + sin2θ) = 1 + 3

r2 = 4

⇒ r = 2

∴ form (1) and (2),

cosθ = 1/2, sinθ = √3/2

∴ θ = π/3

∴ z = 1 + i√3 = 2(cos π/3 + isin π/3)


The complex number z= 1 + √3 is represented by P(2,π/3) into polar.

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