Hello. Any help would be appreciated on showing me how to solve this problem.
Form a polynomial with real coefficients having a degree of 3 and zeros -5 and 1+i.
Factors of the required polynomial are $\displaystyle (z + 5)$, $\displaystyle (z - [1 + i])$ and $\displaystyle (z - [1 + i])$. Note that $\displaystyle (z - [1 + i])(z - [1 - i]) = (z - 1)^2 + 1 = z^2 - 2z + 2$.