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Points P and Q represent the complex numbers z1 and z2. Given that |1/z1 + 1/z2| = |1/z1 - 1/z2|, find the circumcentre of triangle OPQ, where O is the origin.

1. (z1 - z2)/2
2. (z1 + z2)/2
3. (z1 + z2)/3
4. z1 + z2

Correct answer: (z1 + z2)/2

Solution

The condition forces OP perpendicular to OQ, so the angle at O is 90 deg. In a right triangle the circumcentre is the midpoint of the hypotenuse PQ, i.e. (z1+z2)/2.

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