$\text{ Let }\mathrm{A}\text{ and }\mathrm{B}\text{ be two sets of complex numbers such that }$

$\mathrm{A}=\left\{\mathrm{z}:|\mathrm{z}{|}^3-2|\mathrm{z}{|}^2+3\mathrm{i}\left|\mathrm{z}\right|-6\mathrm{i}=0\right\}\text{ and }\mathrm{B}=\left\{\mathrm{z}:\left|{\mathrm{z}}^2-4\right|+\left|{\mathrm{z}}^2+4\right|\le 4\left|\mathrm{z}\right|\right\}.\text{ Find the area of }$$\text{ the polygon formed by joining all the points of }\mathrm{A}\cap \mathrm{B}\text{. }$