Mathematics - Complex Number Question with Solution | TestHub

Since, $z\bar{z}\left(z^2+{\bar{z}}^2\right)=250$ $$\begin{array}{rl}& \Rightarrow 2\left(x^2+y^2\right)\left(x^2-y^2\right)=350\\ & \Rightarrow \left(x^2+y^2\right)\left(x^2-y^2\right)=175\end{array}$$ Since, $x,y\in I$, the only possible case which gives integral solution, is and $\begin{array}{rl}{x}^2+y^2& =25\\ x^2-y^2& =7\end{array}$ From Eqs. (i) and (ii), we get $x^2=16;y^2=9\Rightarrow x=\pm 4;y=\pm 3$ $\therefore$ Area of rectangle $=8\times 6=48$