Question:
Solution:
The midpoint of the line segment joining two complex numbers a+bi and s+ti is the average of the numbers at the endpoints. That is, the Midpoint Formula is:
[tex]M\text{ = }\frac{a+s}{2}+\frac{(b+t)}{2}i[/tex]
note that in this case:
a+bi = 3 + 8i
and
s+ti = 2-i = 2-(1)i
thus, the midpoint between these two complex numbers is:
[tex]M\text{ = }\frac{a+s}{2}+\frac{(b+t)}{2}i\text{ = }\frac{3+2}{2}+\frac{(8-1)}{2}i[/tex]
that is:
[tex]\text{ }\frac{3+2}{2}+\frac{(8-1)}{2}i\text{ = }\frac{5}{2}+\frac{7}{2}i[/tex]
so that, the correct answer is:
[tex]\frac{5}{2}+\frac{7}{2}i[/tex]
