What is the midpoint of the segment joining 12 + 12i and 24 − 8i?

Answer 1

take the average of the real coordinates: (24+12)/2 = 36/2 = 18

take the average of the imaginary coordinates: (12i - 8i)/2 = 4i/2 = 2i

midpoint is (18,2i)

graph the line and plot the points with the y axis as the imaginary axis and x-axis as the real axis

plot it carefully enough and you can see (18,2i) is about right.

Answer 2

The x coordinate is halfway between 12 and 24, the y (imaginary) coordinate is halfway between 12i and -8i.

(24+12)/2 + i(12+(-8))/2 = ______?