Write the expression in the standard form a + bi.
-$( \sqrt { 3 } + i ) ^ { 5 }$
A) $- 16 \sqrt { 3 } + 16 i$
B) $16 - 16 \sqrt { 3 } \mathrm { i }$
C) $9 \sqrt { 3 } + 5 i$
D) $16 \sqrt { 3 } - 16 \mathrm { i }$

Question

Quizplus · Accepted Answer

To express $( \sqrt { 3 } + i ) ^ { 5 }$ in the form $a + bi$, we can first express $\sqrt { 3 } + i$ in polar form, $r(\cos \theta + i\sin \theta)$, where $r = 2$ and $\theta = \frac{\pi}{6}$. Then, using De Moivre's Theorem, raise it to the 5th power. The result is $32(\cos \frac{5\pi}{6} + i\sin \frac{5\pi}{6})$, which simplifies to $-16\sqrt{3} + 16i$.

Write the Expression in the Standard Form a + Bi (3+i)5( \sqrt { 3 } + i ) ^ { 5 }(3​+i)5

Write the Expression in the Standard Form a + Bi $( \sqrt { 3 } + i ) ^ { 5 }$