Mathematics - Complex Number Question with Solution | TestHub

If $\left|Z_1-Z_2\right|=\sqrt{25-12\sqrt{3}}$, and $\frac{Z_1-Z_3}{Z_2-Z_3}=\frac{3}{4}{e}^{i\frac{\pi }{6}}$, then area of triangle (in square units) whose vertices are represented by $Z_1,Z_2,Z_3$ is $\_\_\_\_$