polynomial of lowest degree with with lowest possible integer coefficients and zeros of -5i and 3+4i

Answer 1

imaginery zeros have conjugate pairs that are also zeros. So that's 4th degree polynomial

with zeros -5i, +5i, 3+4i and 3-4i x=3+4i, x-3=4i, x^2 -6x + 9 = -16, x^2-6x+25 = 0

factors are (x+5i)(x-5i)(x^2-6x+25, multiply them out to get the 4th degree polynomial

= (x^2 +25)(x^2 -6x +25)

= x^4 -6x^3 + 50x^2 -150x +625