Find Powers of Complex Numbers in Polar Form
-$$( - 2 + 2 i \sqrt { 3 } ) ^ { 3 }$$
A) 64
B) 8
C) $- 2 + 2 \mathrm { i } \sqrt { 3 }$
D) $8 + 6 i \sqrt { 3 }$

Question

Quizplus · Accepted Answer

The complex number $-2 + 2i\sqrt{3}$ can be converted to polar form as $4(\cos(120^\circ) + i\sin(120^\circ))$. Raising it to the power of 3, we use De Moivre's theorem: $[4(\cos(120^\circ) + i\sin(120^\circ))]^3 = 4^3[\cos(360^\circ) + i\sin(360^\circ)] = 64$.

Find Powers of Complex Numbers in Polar Form - (−2+2i3)3( - 2 + 2 i \sqrt { 3 } ) ^ { 3 }(−2+2i3​)3

Find Powers of Complex Numbers in Polar Form
- $( - 2 + 2 i \sqrt { 3 } ) ^ { 3 }$