How to solve the complex equation $ω^2=-11/4+15i$

The question is stated as following:

"First, solve the equation:

$ω^2=-11/4+15i$

and after, with the help of that, solve:

$z^2-(3-2i)z+(4-18i)=0$"

The problem for me lies in solving the system of equations for ω;

$Re:a^2-b^2=-11/4$ and $Im:2ab=15$

Where I eventually end up with the fourth degree equation: $4b^4+11b^2+15^2=0$ which I don't know how to solve, is this solveable or am I on the wrong track? I would very much appreciate some help, thank you for your time.