Find Roots of Complex Numbers in Polar Form
-The complex cube roots of $- 8 \mathrm { i }$ (rectangular form)
A) $2 i , - \sqrt { 3 } - i , \sqrt { 3 } - i$
B) $2 i , - \sqrt { 3 } + i , - \sqrt { 3 } + i$
C) $- 2 i , \sqrt { 3 } - i , \sqrt { 3 } - i$
D) $- 2 i , \sqrt { 3 } + i , \sqrt { 3 } + i$

Question

Quizplus · Accepted Answer

The complex number $-8i$ in polar form is $8(\cos\frac{3\pi}{2} + i\sin\frac{3\pi}{2})$. Using De Moivre's theorem to find the cube roots, we divide the angle by 3 and find the roots at $0 + \frac{2\pi k}{3}$ for $k=0,1,2$. The roots are $2i, -\sqrt{3} - i, \sqrt{3} - i$.

Find Roots of Complex Numbers in Polar Form -The Complex −8i- 8 \mathrm { i }−8i

Find Roots of Complex Numbers in Polar Form
-The Complex $- 8 \mathrm { i }$