A segment in the complex plane has a midpoint at 3 – 2i. If one endpoint of the segment is at 7 + i, what is the other endpoint?

The midpoint is the average of the endpoints. Let the other endpoint be z. Then (7 + i + z)/2 = 3 − 2i, so z = 2(3 − 2i) − (7 + i). This gives z = 6 − 4i − 7 − i = −1 − 5i, which is choice A.

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