Question

Using Pascal's Triangle, expand and simplify the complex binomial (3t - 2i)^5

(the i is an imaginary number, not a variable)

Answer 1

`\displaystyle(3t-2i)^5=\binom50(3t)^5(-2i)^0+\binom51(3t)^4(-2i)^1+\binom52(3t)^3(-2i)^2+\binom53(3t)^2(-2i)^3+\binom54(3t)^1(-2i)^4+\binom55(3t)^0(-2i)^5`

where
`\dbinom50,\dbinom51,\ldots` are the numbers in the fifth row of Pascal's triangle. They're given by


`\dbinom5n=(5!)/(n!(5-n)!)`

So the expansion is


`\displaystyle(3t-2i)^5=243t^5-810it^4-1080t^3+720it^2+240t-32i`