# If $|z+\overline z|+|z-\overline z|=8$ then $z$ lies on ?

$\begin{array}{1 1}(A)a circle \\ (B) a straight line \\ (C) a square \\(D) an ellipse \end{array}$

Toolbox:
• $|x|+|y|=k$ represents a square.
Given: $|z+\overline z|+|z-\overline z|=8$
Let $z=x+iy$
$\Rightarrow\:2|x|+2|iy|=8$
$\Rightarrow\:|x|+|y|=4$
This represents a square.