how do you write simples polynomial function with the given zero

Question

1-i and 2

Answer 1

(x-1+i)(x-2)=0

multiply it out, and gather terms.

Answer 2

However, if you want a polynomial with real coefficients, you need another zero: the conjugate of 1-i = 1+i

SO, your polynomial is then

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