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in Complex Numbers by (50.7k points)
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Write z = (–1 + i√3) in polar form.

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We have, z = (–1 + i√3)

Let -1 = r cosθ and √3 = r sinθ

By squaring and adding, we get

(-1)2 + (√3)2 = (r cosθ)2 + (r sinθ)2

⇒ 1+3 = r2 (cos2θ + sin2θ)

⇒ 4 = r2

⇒ r = 2

∴ cosθ = -1/2 and sinθ = √3/2

Since, θ lies in second quadrant, we have

θ = π - π/3 = 2π/3

Thus, the required polar form is 2[cos\(\frac{2\pi}{3}\)+i sin\(\frac{2\pi}{3}\)]

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