Question

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

1 + 2i
2 + i
2 + 4i
5 + 4i

Answer 1

The middle of 6-2i and -4+6i is 1+2i :)

Answer 2

Mid point of 6 – 2i and –4 + 6i is 1+2i

A is correct.

Explanation:

We are given two complex number and need to find mid point of them

`z_1=a_1+ib_1\text{ and }z_2=a_2+ib_2`

`\text{Mid point z}=(z_1+z_2)/(2)`

`z=(a_1+a_2)/(2)+i(b_1+b_2)/(2)`

where,
`z_1=6-2i\text{ and } z_2=-4+6i`

Mid point of 6 – 2i and –4 + 6i

`z=(6-4)/(2)+i(-2+6)/(2)`

`z=1+2i`

Thus, Mid point of 6 – 2i and –4 + 6i is 1+2i