form a polynomial with real coefficients have given degree and zeros.

Question

degree 5, zeros 9, -i; 8+i

please show work

Answer 1

complex roots are in pairs, so we have
(x-9)(x+i)(x-i)(x-(8+i))(x-(8-i))
(x-9)(x^2+1)((x-8)^2 + 1)

. . .