Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 1+i,1

Answer 1

If 1+i is a zero, then so is 1-i, making (x^2 -2x +2) a factor, the other factor is x-1

(x^2-2x+2)(x-1) = x^3 -3x^2 +4x -2 is the least degree polynomial with the required zero 1+i and 1,

if the coefficients are real and rational.

x-1 = 0

x = 1

x=1 -i

x-1 = -i

(x-1)^2 = -1

x^2 -2x +1 = -1

x^2 -2x +2 = 0