Represent the complex number z = 1 + i√3 in the polar form.
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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, r 2 (cos 2 θ + sin 2 θ) = 1 + 3 r 2 = 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.