Mathematics - Complex Number Question with Solution | TestHub

Let a complex number, $z=x+iy$ $\Rightarrow \bar{z}=\bar{x}-iy$ Then, vertices of rectangle for $z,\bar{z},-z,-\bar{z}$ are $(x,y),(x,-y),(-x,-y),(-x,y)$Now, Area of rectangle $=(2x)(2y)=4xy$ It is given that, Area $=2\sqrt{3}=4xy\Rightarrow 2xy=\sqrt{3}$ $\therefore x=\frac{1}{2},y=\sqrt{3}\therefore z=\frac{1}{2}+\sqrt{3}i$