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

I don't understand how to do this.

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- Jan 13th 2011, 08:41 PMCthulFinding real numbers of a complex polynomial
Find the value of $\displaystyle a$ and $\displaystyle b$ $\displaystyle (a,b \in R)$ given that $\displaystyle 2i$ and $\displaystyle 3i$ are roots of $\displaystyle P(z)=z^{3}+aiz^{2}+bz-12i$

I don't understand how to do this. - Jan 13th 2011, 08:53 PMProve It
Hint: If $\displaystyle \displaystyle 2i$ is a root then $\displaystyle \displaystyle P(2i) = 0$, and if $\displaystyle \displaystyle 3i$ is a root then $\displaystyle \displaystyle P(3i) = 0$.

You should end up with two equations in two unknowns ($\displaystyle \displaystyle a,b$) that you can solve simultaneously. - Jan 13th 2011, 09:05 PMCthul
How stupid of me. Thank you.