Use the Binomial Theorem to expand the following complex number. Write your answer in standard form.
$\left( - \frac { 3 } { 7 } - \frac { \sqrt { 7 } } { 7 } i \right) ^ { 3 }$
A) $\frac { 36 } { 343 } - \frac { 20 \sqrt { 7 } } { 343 } i$
B) $\frac { 36 } { 343 } + \frac { 20 \sqrt { 7 } } { 49 } i$
C) $- \frac { 36 } { 49 } - \frac { 20 \sqrt { 7 } } { 343 } i$
D) $- \frac { 27 } { 343 } + \frac { \sqrt { 7 } } { 49 } i$
E) $- \frac { 27 } { 343 } - \frac { \sqrt { 7 } } { 49 } i$

Question

Quizplus · Accepted Answer

To expand $\left( - \frac { 3 } { 7 } - \frac { \sqrt { 7 } } { 7 } i \right) ^ { 3 }$ using the Binomial Theorem, we calculate each term of the expansion. The real part comes from the terms where the powers of $i$ are even, and the imaginary part comes from the terms where the powers of $i$ are odd. The expansion yields $\frac { 36 } { 343 } - \frac { 20 \sqrt { 7 } } { 343 } i$ in standard form.

Use the Binomial Theorem to Expand the Following Complex Number (−37−77i)3\left( - \frac { 3 } { 7 } - \frac { \sqrt { 7 } } { 7 } i \right) ^ { 3 }(−73​−77​​i)3

Use the Binomial Theorem to Expand the Following Complex Number $\left( - \frac { 3 } { 7 } - \frac { \sqrt { 7 } } { 7 } i \right) ^ { 3 }$