Answer: The midpoint of the line segment is [tex](-7.5+2.5i).[/tex]
Step-by-step explanation: We are given to find the mid-point of the line segment with endpoints as follows:
[tex]A=-11+i,\\\\B=-4+4i.[/tex]
We know that a complex number can be treated as a co-ordinate of a point in the two dimensional plane.
That is, if (x, y) is any point in the XY-plane, then we can write
(x, y) ⇒ x + yi.
So, the points 'A' and 'B' can be written as
[tex]A=-11+i=(-11,1),\\\\B=-4+4i=(-4,4).[/tex]
Therefore, the co-ordinates of the mid-point of the line segment with endpoints 'A' and 'B' are
[tex]\left(\dfrac{-11+(-4)}{2},\dfrac{1+4}{2}\right)=\left(\dfrac{-15}{2},\dfrac{5}{2}\right)=(-7.5,2.5).[/tex]
So, (-7.5, 2.5) is the mid-point of the line segment AB.
Writing the co-ordinates of the mid-point in the form of a complex number, we have
(-7.5, 2.5) ⇒ -7.5 + 2.5i.
Thus, the required midpoint is [tex]-7.5+2.5i.[/tex]
