Find the indicated power using De Moivre’s Theorem (−5−5sqrt 3i)^3

-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 ) = π - arctan(√3) = 2π/3

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

so that the polar form of the number is

-5 - 5√3 i = 10 exp(2π/3 i )

By DeMoivre's theorem, we have

(-5 - 5√3 i )³ = 10³ exp(3 × 2π/3 i ) = 1000 exp(2πi ) = 1000

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

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