A line segment in the complex plane has endpoints -6-7i and 3-i Find its midpoint. Write your answer in the form a+bi Simplify all fractions. square

## Step 1: Formula for the Midpoint of a Line Segment in the Complex Plane<br />### The midpoint of a line segment with endpoints $z_1 = a + bi$ and $z_2 = c + di$ in the complex plane is given by the formula: $M = \frac{z_1 + z_2}{2} = \frac{(a+c)}{2} + \frac{(b+d)}{2}i$.<br /><br />## Step 2: Applying the Midpoint Formula<br />### Given endpoints are $z_1 = -6 - 7i$ and $z_2 = 3 - i$. Here, $a = -6$, $b = -7$, $c = 3$, and $d = -1$. Substituting these values into the midpoint formula: $M = \frac{(-6 + 3)}{2} + \frac{(-7 + (-1))}{2}i = \frac{-3}{2} + \frac{-8}{2}i = -\frac{3}{2} - 4i$.