Let $\alpha, \beta$ be the roots of the equation $x^{2}-\mathrm{ax}-\mathrm{b}=0$ with $\operatorname{Im}(\alpha)<\operatorname{Im}(\beta)$. Let $\mathrm{P}_{\mathrm{n}}=\alpha^{\mathrm{n}}-\beta^{\mathrm{n}}$. If $\mathrm{P}_{3}=-5 \sqrt{7} i, \mathrm{P}_{4}=-3 \sqrt{7} i, \mathrm{P}_{5}=11 \sqrt{7} i$ and $\mathrm{P}_{6}=45 \sqrt{7} i$, then $\left|\alpha^{4}+\beta^{4}\right|$ is equal to $\_\_\_\_$ .