The given points are
[tex](-5-2i),(3+8i)[/tex]These are complex numbers. They work as two-coordinates points because complex numbers have a real part and a complex part. The real part is the horizontal coordinate, and the complex part is the vertical coordinate.
To find the midpoint, we use the following formula
[tex]\begin{gathered} M=(\frac{-5+3}{2},\frac{-2+8}{2}i) \\ M=(\frac{-2}{2},\frac{6}{2}i) \\ M=(-1,3i) \end{gathered}[/tex]