Mathematics

Problem

Let

Z_i \{i = 1, 2, 3, 4\}

represent the vertices of a square all of which lies on sides of a triangle with vertices

(0, 0), (2, 1)

and

(3, 0)

. Given that

Z_1

and

Z_2

are real. If

Z_3 = a + ib, Z_4 = c + id, a, b, c, d \in \mathbb{R}

, then