10
QuizMultiple Choice

Powers and Roots of Complex Numbers — Unit test

Question 10 • Precalculus

The following statements are about finding a midpoint of a segment in the complex plane. Which statement is false?

Answer
A
The midpoint is the average of the endpoints.
B
First add the endpoints and then multiply by 1/2.
C
First subtract the endpoints and then divide by 2.
D
The midpoint of complex conjugates will lie on the x-axis.

Explanation

The midpoint of endpoints z₁ and z₂ is (z₁ + z₂)/2, so you add the endpoints and multiply by 1/2. Subtracting the endpoints and dividing by 2 gives half the difference, not the midpoint in general. For conjugates a + bi and a − bi, their midpoint is a, which lies on the x-axis.

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