Use the Binomial Theorem to expand the complex number.Simplify your result. $( 3 - i ) ^ { 5 }$
A) $405 i + 12$
B) $90 i + 12$
C) $316 i + 405$
D) $- 12 - 316 i$
E) $316 + 12 i$

Question

Use the Binomial Theorem to expand the complex number.Simplify your result.​ $( 3 - i ) ^ { 5 }$ ​
A) $405 i + 12$
B) $90 i + 12$
C) $316 i + 405$
D) $- 12 - 316 i$
E) $316 + 12 i$

Quizplus · Accepted Answer

The Binomial Theorem can be used to expand $(3 - i)^5$. The expansion will involve terms of the form $\binom{5}{k} (3)^{5-k}(-i)^k$, where $k$ ranges from 0 to 5. Simplifying this expansion, we find that the real parts and the imaginary parts combine to give $-12 - 316i$.

Use the Binomial Theorem to Expand the Complex Number (3−i)5( 3 - i ) ^ { 5 }(3−i)5

Use the Binomial Theorem to Expand the Complex Number $( 3 - i ) ^ { 5 }$