Question

How do you multiply `(x+5)(x-3)(x-4+i)`?

Answer 1

`x^3-2x^2-23x+60 +ix^2+2ix-15i`

Explanation:

First, multiply the first and second expressions:

`(x+5)(x-3) = x^2 -3x+5x-15 = x^2+2x-15`

Having the result of the multiplication, now multiply the result by the third expression:

`(x^2+2x-15)(x-4+i)`
`= (x^3-4x^2+ix^2) + (2x^2-8x+2ix) + (-15x + 60 - 15i)`
`= x^3-2x^2-23x+60 +ix^2+2ix-15i`