Use the Binominal Theorem to expand the complex number.Simplify your result. $( 4 - 6 i ) ^ { 4 }$
A) $- 256 + 1536 i + 3456 + 3456 i ^ { 3 } - 1296$
B) $256 + 1536 i - 3456 + 3456 i ^ { 3 } + 1296$
C) $- 256 - 1536 i + 3456 - 3456 i ^ { 3 } - 1296$
D) $256 - 1536 i - 3456 - 3456 i ^ { 3 } + 1296$
E) $1296 - 3456 i - 3456 - 1536 i ^ { 3 } + 256$

Question

​Use the Binominal Theorem to expand the complex number.Simplify your result.​ $( 4 - 6 i ) ^ { 4 }$ ​
A)​ $- 256 + 1536 i + 3456 + 3456 i ^ { 3 } - 1296$
B)​ $256 + 1536 i - 3456 + 3456 i ^ { 3 } + 1296$
C)​ $- 256 - 1536 i + 3456 - 3456 i ^ { 3 } - 1296$
D)​ $256 - 1536 i - 3456 - 3456 i ^ { 3 } + 1296$
E)​ $1296 - 3456 i - 3456 - 1536 i ^ { 3 } + 256$

Quizplus · Accepted Answer

Using the Binomial Theorem, $(4 - 6i)^4$ expands to $256 - 1536i - 3456 - 3456i^3 + 1296$. Simplifying using $i^2 = -1$ and $i^3 = -i$, the correct result is option D.

​Use the Binominal Theorem to Expand the Complex Number (4−6i)4( 4 - 6 i ) ^ { 4 }(4−6i)4

Use the Binominal Theorem to Expand the Complex Number $( 4 - 6 i ) ^ { 4 }$