Question

find a polynomial with real coefficients having 1-i and 3+2i as it's zeros

Answer 1

Well, I thought this would work, but wolfram claims it isn't all real coefficients...\[(x-(1-i))(x+(1-i))(x-(3+2i))(x+(3+2i))\]I though it would work because if you have a complex root, you also have to have it's negative, so I multiplied all the irreducible polynomials of degree one with \((1-i), (-1+i), (3+2i), (-3-2i)\) as roots together, but apparently you need more.