Answer:
[tex]x^2-4x+8[/tex]
[tex]x^2+4[/tex]
[tex]x^2+2x+2[/tex]
Step-by-step explanation:
(1) (x-2+2i) (x-2-2i)
Multiply each term inside second parenthesis
[tex]x^2-2x-2ix -2x+4+4i+2ix-4i-4i^2[/tex]
Combine like terms. the value of i^2=-1
[tex]x^2-4x+4-4(-1)[/tex]
[tex]x^2-4x+8[/tex]
(2) (x+2i)(x-2i)
[tex]x^2- 2ix +2ix -4i^2[/tex]
Replace i^2 by -1
[tex]x^2+4[/tex]
(3) (x+1+i)(x+1-i)
Multiply each term inside second parenthesis
[tex]x^2+x-ix+x+1-i+ix+i-i^2[/tex]
Combine like terms. the value of i^2=-1
[tex]x^2-4x+4-4(-1)[/tex]
[tex]x^2+2x+2[/tex]
