Question

How do I simplify

(x+1)(x(-4-5i))(x-(4+5i))?

Answer 1

I don't know about "simplify" bu to expand it, try this:

You know that
(a-b)(a+b) = a^2-b^2
(a-bi)(a+bi) = a^2+b^2
So,

(x+1)(x(-4-5i))(x-(4+5i))
= (x+1)((x-4)-5i)((x-4)+5i)
= (x+1)((x-4)^2 - (5i)^2)
= (x+1)(x^2-8x+16 + 25)
= (x+1)(x^2-8x+41)
= x^3-7x^2+33x+41
=