Find the given power. Write answer in rectangular form.
-$$( - \sqrt { 3 } + i ) ^ { 6 }$$
A) $64 - 64 \sqrt { 3 } i$
B) $- 64$
C) $- 64 \sqrt { 3 } + 64 i$
D) $64 \mathrm { i }$

Question

Quizplus · Accepted Answer

The complex number $-\sqrt{3} + i$ can be expressed in polar form and raised to the 6th power using De Moivre's Theorem. The magnitude is 2 and the angle is $150^\circ$. Raising to the 6th power gives a magnitude of $64$ and an angle of $900^\circ$, which is equivalent to $180^\circ$, resulting in $-64$ in rectangular form.

Find the Given Power (−3+i)6( - \sqrt { 3 } + i ) ^ { 6 }(−3​+i)6

Find the Given Power $( - \sqrt { 3 } + i ) ^ { 6 }$