Question

expand using the binomial theorem:
(4-5i)^3
Remember that i=sqrt -1

Answer 1

(4-5i)^3 = -236-115i

Answer 2

that's not what expanding is, but thanks for trying.

Answer 3

By the binomial theorem:
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

So here
\[(4-5i)^3 = 4^3 + 3.4^2(-5i) +3.4.(-5i)^2 + (-5i)^3\]
\[ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 64 + -240i + 300i^2 + -125i^3 \]
\[ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 64 + -240i -300 + 125i \]
\[ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = -236 - 115i \]