Perform the indicated operation. Write the result in standard form.
-$[ - 4 + 4 i \sqrt { 3 } ] ^ { 3 }$
A) 512
B) $- 4 + 4 i \sqrt { 3 }$
C) 64
D) $64 + 12 i \sqrt { 3 }$

Question

Quizplus · Accepted Answer

To solve $[ - 4 + 4 i \sqrt { 3 } ] ^ { 3 }$, we first recognize the given complex number is in the form $a + bi$, where $a = -4$ and $b = 4\sqrt{3}$. The cube of this complex number can be calculated directly or by recognizing it as $(2\sqrt{3})^3(-2 - 2i\sqrt{3})^3$, which simplifies to $8\sqrt{27}(-8 - 8\sqrt{3}i - 12)$, ultimately simplifying to $512$, since the imaginary parts cancel out and the real parts add up to $512$.

Perform the Indicated Operation [−4+4i3]3[ - 4 + 4 i \sqrt { 3 } ] ^ { 3 }[−4+4i3​]3

Perform the Indicated Operation $[ - 4 + 4 i \sqrt { 3 } ] ^ { 3 }$