Find the product. Write the answer in standard form.
-$( 2 - 4 i ) ^ { 3 }$
A) $i ^ { 3 } + 96 i ^ { 2 } - 48 i + a ^ { 3 }$
B) $- 88 - 48 i + i ^ { 3 }$
C) $- 88 + 16 i$
D) $- 88 - 145 \mathrm { i }$

Question

Quizplus · Accepted Answer

To find the product $(2 - 4i)^3$, we first expand it using the binomial theorem or by multiplying it step by step. The calculation is as follows: $(2 - 4i)^2 = 4 - 16i + 16i^2 = 4 - 16i - 16 = -12 - 16i$. Then, multiplying this result by $(2 - 4i)$ again: $(-12 - 16i)(2 - 4i) = -24 + 48i - 32i + 64i^2 = -24 + 16i - 64 = -88 + 16i$. Thus, the product in standard form is $-88 + 16i$.

Find the Product (2−4i)3( 2 - 4 i ) ^ { 3 }(2−4i)3

Find the Product $( 2 - 4 i ) ^ { 3 }$