Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi.
-$\left( 5 \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right) \right) ^ { 3 }$
A) $- 108.25 - 62.5 \mathrm { i }$
B) $- 12.99 - 62.5 \mathrm { i }$
C) $- 170.75$
D) $- 12.99 + 62.5 \mathrm { i }$

Question

Quizplus · Accepted Answer

De Moivre's Theorem states that $(r(\cos \theta + i\sin \theta))^n = r^n (\cos(n\theta) + i\sin(n\theta))$. Applying this to the given complex number, we get $5^3(\cos(3 \times 70^\circ) + i\sin(3 \times 70^\circ)) = 125(\cos(210^\circ) + i\sin(210^\circ))$, which simplifies to $-108.25 - 62.5i$.

Use De Moivre's Theorem to Find the Indicated Power of the Complex