Use the Binomial Theorem to expand the complex number. Simplify your result.
$$( 5 + 4 i ) ^ { 4 }$$
A) $- 1519 + 720 i$
B) $- 1519 - 720 i$
C) $1519 + 720 i$
D) $1519 - 720 i$
E) 625

Question

Quizplus · Accepted Answer

The Binomial Theorem gives $(5 + 4i)^4 = \sum_{k=0}^{4} \binom{4}{k} (5)^{4-k} (4i)^k$. Calculating each term and summing them gives $-1519 + 720i$.

Use the Binomial Theorem to Expand the Complex Number (5+4i)4( 5 + 4 i ) ^ { 4 }(5+4i)4

Use the Binomial Theorem to Expand the Complex Number $( 5 + 4 i ) ^ { 4 }$