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Answer :

LammettHashgo

-5 - 5√3 i = -5 (1 + √3 i )

We have modulus

|-5 (1 + √3 i )| = 5 √(1² + (√3)²) = 5√4 = 10

and argument

arg(-5 - 5√3 i ) = Ο€ - arctan(√3) = 2Ο€/3

(we subtract from Ο€ because the given complex number lies in the third quadrant of the complex plane, whereas the arctan function only returns angles between -Ο€/2 and Ο€/2)

so that the polar form of the number is

-5 - 5√3 i = 10 exp(2Ο€/3 i )

By DeMoivre's theorem, we have

(-5 - 5√3 i )Β³ = 10Β³ exp(3 Γ— 2Ο€/3 i ) = 1000 exp(2Ο€i ) = 1000

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