Elijah made an error of subtracting the numbers and not including the imaginary sign (letter i)
The correct midpoint is (6, 3i)
Explanation:The two points are 8 + 4i and 4 + 2i
Elijah got the midpoint as (2, 1).
To determine Elijah's error, let's calculate the midpoint of a complex number:
[tex]\text{Midpoint = (}\frac{a\text{ + b}}{2}),\text{ (}\frac{c\text{ + d}}{2})i[/tex]let 8 + 4i = a + ci
let 4 + 2i = b + di
The real numbers will be added together. The imaginary numbers will also be added together.
substituting the values in the formula:
[tex]\begin{gathered} \text{Midpoint = (}\frac{8\text{ + 4}}{2}),\text{ (}\frac{4\text{ + 2}}{2})i \\ \text{Midpoint = }\frac{12}{2},\text{ }\frac{6}{2}i \\ \\ \text{Midpoint = (6, 3i)} \end{gathered}[/tex]Elijah made an error of subtracting the numbers. Also Elijah didn't include the letter representing the imaginary numbers (i).
The correct midpoint is (6, 3i)