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 allows us to expand $(a + b)^n$ into a sum involving terms of the form $\binom{n}{k} a^{n-k}b^k$. For $(3 - i)^5$, we calculate each term of the expansion. The real parts and imaginary parts will combine separately. After calculation, the expansion simplifies to $-12 - 316i$.

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 $( 3 - i ) ^ { 5 }$