1. **State the problem:** Find the midpoint of the segment connecting the complex numbers $z_1 = 0 + 4i$ and $z_2 = 0 - 5i$ in the complex plane. 2. **Formula for midpoint:** The midpoint $M$ of two complex numbers $z_1 = a + bi$ and $z_2 = c + di$ is given by $$M = \frac{z_1 + z_2}{2} = \frac{(a+c) + (b+d)i}{2}$$ 3. **Apply the formula:** Here, $z_1 = 0 + 4i$ and $z_2 = 0 - 5i$, so $$M = \frac{(0 + 0) + (4 + (-5))i}{2} = \frac{0 + (-1)i}{2} = \frac{-1i}{2}$$ 4. **Simplify:** $$M = 0 + \frac{-1}{2}i = -\frac{1}{2}i$$ 5. **Final answer:** The midpoint is $$\boxed{0 - \frac{1}{2}i}$$ This means the midpoint lies on the imaginary axis at $-\frac{1}{2}i$.