Consider the complex numbers \( z_1 = 1 + i \), \( z_2 = 1 - i \), \( z_3 = -1 + i \), and \( z_4 = -1 - i \). These points form the vertices of a square in the complex plane. Compute the area of the square, and verify that the diagonals intersect at a right angle. Let's think step by step and output the final answer within \boxed{}.
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