Problem:
Four complex numbers lie at the vertices of a square in the complex plane. Three of the numbers are and . The fourth number is
Answer Choices:
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E.
Solution:
Two given points, and , are symmetric with respect to the origin, and the distances from the origin to all three points are equal. Therefore the origin is the center of the square, and the fourth vertex must be symmetric to around it. Thus the fourth vertex is .
Plotting the given three points makes it graphically clear where the fourth point must go.