Question

Find the polynomial with leading coefficient 1 that has degree 3 and zeros 1 and 1-i.

Answer 1

It's a polynomial with degree 3, so it has, at most, three distinct roots. 2 are already give. The third root is the conjugate of 1-i which is 1+i. So, a polynomial, that satisfies the given conditions with leading coefficient 1 is:
\[(x-1)(x-(1-i))(x-(1+i))=(x-1)(x-1+i)(x-1-i)\]