Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

If -1+root -3 = r^ei theta, then theta is equal (1) pi/3 (2) -pi/3 (3) 2 pi/3 (4) -2pi/3

Solution:

Given -1+√-3 = re

-1+√-3 = -1+√3i

-1+√3i = r(cos θ+i sin θ)

r cos θ = -1

r sin θ = √3

Squaring and adding

r2(cos2θ+sin2θ) = 1+3

r2 = 4

r = 2

cos θ = -½

sin θ = √3/2

θ lies in second quadrant.

θ = π-π/3

= 2π/3

Hence option (3) is the answer.

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