Question

Use DeMoivre's Theorem:
((sqrt3)+(i))^3

Answer 1

\[(r <\theta)^{n} = (r(\cos(\theta)+isin(\theta))^{n} = r ^{n}(\cos(n \theta) +isin(n \theta))\]

Answer 2

\[\sqrt{3} +i = 2 \angle 30^{o}\]

Answer 3

\[(r \angle \theta)^n = r^n \angle(n \theta) \]

Answer 4

\[2 \angle 30^o =2^3 \angle (3*30^o) = 8 \angle 90^o \]

Answer 5

8(cos(pi)+i sin(pi))
Is that right?

Answer 6

it's in polar form

Answer 7

pi/2

Answer 8

Ahh...so confusing. sorry about this >_<
So it would be 8(cos(pi/2)+i sin(pi/2))

Answer 9

yup