# Thread: Finding real numbers of a complex polynomial

1. ## Finding real numbers of a complex polynomial

Find the value of $a$ and $b$ $(a,b \in R)$ given that $2i$ and $3i$ are roots of $P(z)=z^{3}+aiz^{2}+bz-12i$

I don't understand how to do this.

2. Hint: If $\displaystyle 2i$ is a root then $\displaystyle P(2i) = 0$, and if $\displaystyle 3i$ is a root then $\displaystyle P(3i) = 0$.

You should end up with two equations in two unknowns ( $\displaystyle a,b$) that you can solve simultaneously.

3. How stupid of me. Thank you.