Let α, β be the roots of the equation x^2-√ 6 x+3=0 such that Im (α)> Im (β). Let a, b be integers not divisible by 3 and n be a natural number such…

Let $\displaystyle \alpha, \beta$ be the roots of the equation $\displaystyle x^2-\sqrt{6} x+3=0$ such that $\displaystyle \operatorname{Im}(\alpha)>\operatorname{Im}(\beta)$. Let $\displaystyle a, b$ be integers not divisible by $\displaystyle 3$ and $\displaystyle n$ be a natural number such that $\displaystyle \frac{\alpha^{99}}{\beta}+\alpha^{98}=3^n(a+i b), i=\sqrt{-1}$. Then $\displaystyle n+a+b$ is equal to $\displaystyle \_\_\_\_$.