Use the Binomial Theorem to find the value of the complex number raised to the given power. Recall that $i = \sqrt { - 1 }$
-$$( - 5 + 3 i ) ^ { 4 }$$
A) $- 644 - 960 i$
B) $644 + 960 i$
C) $644 - 960 i$
D) $- 644 + 960 i$

Question

Quizplus · Accepted Answer

Using the Binomial Theorem, $(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$, we expand $(-5 + 3i)^4$ and calculate each term. The real part sums to -644 and the imaginary part sums to -960.

Use the Binomial Theorem to Find the Value of the Complex