Question

given z₁ and z₂, find the midpoint.
z₁ = 0 - 9i and z₂ = 6 - 3i
? + i

Explanation:

Step1: Recall midpoint formula for complex numbers

For two complex numbers \( z_1 = a + bi \) and \( z_2 = c + di \), the midpoint \( z_m \) is given by \( z_m=\frac{z_1 + z_2}{2}=\frac{(a + c)}{2}+\frac{(b + d)}{2}i \).
Here, \( z_1 = 0-9i \) (so \( a = 0 \), \( b=-9 \)) and \( z_2 = 6 - 3i \) (so \( c = 6 \), \( d=-3 \)).

Step2: Calculate real part of midpoint

Real part: \( \frac{0 + 6}{2}=\frac{6}{2}=3 \)

Step3: Calculate imaginary part of midpoint

Imaginary part: \( \frac{-9+(-3)}{2}=\frac{-12}{2}=-6 \)

Answer:

\( 3 + (-6)i \) (or simply \( 3 - 6i \))