Explanation

(c)
Given that, the vertices of quadrilateral are
$A = (1 + 2i),\ B = ( - 3 + i),\ C = ( - 2 - 3i)$ and $D = (2 - 2i)$
Now, $AB = \sqrt{16 + 1} = \sqrt{17},\ \ BC = \sqrt{1 + 16} = \sqrt{17}$
$CD = \sqrt{16 + 1} = \sqrt{17},\ DA = \sqrt{1 + 16} = \sqrt{17}$
$AC = \sqrt{9 + 25} = \sqrt{34},$ $BD = \sqrt{25 + 9} = \sqrt{34}$
$\therefore$ Sides $AB = BC = CD = DA$ and diagonals $AC = BD$
Hence, it is a square