### Instruction: In the complex plane, the line segment with end-points $-11 + 3i$ and $3 - 7i$ is plotted in the complex plane.  Find the complex number corresponding to the mid-point of this line segment.### Response: I know that the complex numbers on the complex plane are represented by their real and imaginary parts as the $x$ and $y$ coordinates, respectively.
So, to find the mid-point of the line segment, I need to find the average of the real parts and the average of the imaginary parts of the end-points.
The real part of $-11 + 3i$ is $-11$, and the real part of $3 - 7i$ is $3$. The average of $-11$ and $3$ is $(-11 + 3)/2 = -4$.
The imaginary part of $-11 + 3i$ is $3$, and the imaginary part of $3 - 7i$ is $-7$. The average of $3$ and $-7$ is $(3 + (-7))/2 = -2$.
Therefore, the complex number corresponding to the mid-point of the line segment is $-4 - 2i$.