Question

VERY IMPORTANT!! PLEASE ANSWER CORRECTLY!!

Answer 1

`x^2-4x+8`

`x^2+4`

`x^2+2x+2`

Explanation:

(1) (x-2+2i) (x-2-2i)

Multiply each term inside second parenthesis

`x^2-2x-2ix -2x+4+4i+2ix-4i-4i^2`

Combine like terms. the value of i^2=-1

`x^2-4x+4-4(-1)`

`x^2-4x+8`

(2) (x+2i)(x-2i)

`x^2- 2ix +2ix -4i^2`

Replace i^2 by -1

`x^2+4`

(3) (x+1+i)(x+1-i)

Multiply each term inside second parenthesis

`x^2+x-ix+x+1-i+ix+i-i^2`

Combine like terms. the value of i^2=-1

`x^2-4x+4-4(-1)`

`x^2+2x+2`