5. b) Find a real polynomial of least degree having 1+i, 2, -i as roots.

My work:

1.

x=1+i

x=2

x= -i

2.

[(x-1)-i]

[(x-2)]

[(x)+i]

3.

Secondly I tried putting them together and got:

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

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

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

I cannot remove the i, please help.