$$x^2 + 4x + 20 = 0$$ $$x=-2 \pm 4i$$
Roots of Quadtratic $z^2 + (4+i+qi)z + 20 = 0$ - Roots are $w$ and $w*$
(a) When $q$ is real, explain why it must be $-1$
Roots are conjugates therefore the coefficient must be real - and to get rid of the imaginary parts $q$ must be $-1$?
(b) Where $w=p+2i$ and $p$ is real, find the values of $q$.
Subbed $p+2i$ into equation to give $p=2$, where it is real. Substitute $2+2i$ into the equation again and get $q=3$, and $q=-8$? Very sure this is not correct - Should be a complex number?