Question

the following statements are about finding a midpoint of a segment in the complex plane. which statement is false?
the midpoint is the average of the endpoints.
first add the endpoints and then multiply by 1/2.
first subtract the endpoints and then divide by 2.
the midpoint of complex conjugates will lie on the x - axis.

Explanation:

1. For complex numbers $z_1 = a+bi$ and $z_2 = c+di$, the midpoint is $\frac{z_1+z_2}{2}$, which is the average of the endpoints, matching the first two statements.
2. Subtracting endpoints and dividing by 2 gives $\frac{z_1-z_2}{2}$, which is half the distance vector between the points, not the midpoint.
3. For complex conjugates $z = a+bi$ and $\overline{z}=a-bi$, their midpoint is $\frac{(a+bi)+(a-bi)}{2}=a$, a real number lying on the x-axis, so the fourth statement is true.

Answer:

First subtract the endpoints and then divide by 2.