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In the complex plane a square P1P2P3P4 has one vertex P1 at (1, 0) and the opposite vertex P3 at (3, 0). Writing each vertex Pn = (xn, yn) for n = 1, 2, 3, 4, compute the product of the four complex numbers (x1 + i*y1)(x2 + i*y2)(x3 + i*y3)(x4 + i*y4).

1. 15
2. 3
3. 5
4. 0

Correct answer: 15

Solution

P1 and P3 are diagonal endpoints, so the centre is (2,0) and the half-diagonal is 1. The other diagonal gives P2=(2,1), P4=(2,-1).

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