Question 32
The equation $6 z^{10}+a_{9} z^{9}+a_{8} z^{8}+a_{7} z^{7}+\ldots+a_{3} z^{3}+a_{2} z^{2}+a_{1} z+9216=0$ is given, where $a_{1}, a_{2}, \ldots, a_{9}$ are real numbers and $z$ is the unknown. We know 5 solutions of the given equation, namely $1+i, 2+2 i, 3+3 i, 4+4 i$ and $\frac{1}{2}$, where $i$ is the imaginary unit. Determine the value of the coefficient $a_{9}$.