Question

What is the midpoint of a segment in the complex plane with endpoints at 6 – 2i and –4 + 6i?

Answer 1

6 - 2i can be written as (6, -2)

where it's in the form of (real, imaginary)
-2i is imaginary, while 6 is real.

Similarly, -4 + 6i can be written as (-4, 6)

You just need to find the midpoint of (6, -2) and (-4, 6)

It would look like this on a complex plane


For example, find the midpoint of 6 + 2i and 8 + 4i
Rewrite them to become (6, 2) and (8, 4)
Find the midpoint
(6 + 8)/2 = 14/2 = 7
(2 + 4)/2 = 6/2 = 3
(7, 3) is the midpoint, which is the same 7 + 3i

OR you could do it this way

(6 + 2i + 8 + 4i)/2 = (14 + 6i)/2
= 7 + 3i

Keep in mind that I did an example and it's not the answer to your question :P