Question

given z₁ and z₂, find the midpoint.
z₁ = 8 + 7i and z₂ = 8 + 0i
? + i

Explanation:

Step1: Recall midpoint formula for complex numbers

For two complex numbers \( z_1 = a + bi \) and \( z_2 = c + di \), the midpoint \( M \) is given by \( M=\frac{z_1 + z_2}{2}=\frac{(a + c)}{2}+\frac{(b + d)}{2}i \).
Here, \( a = 8, b = 7, c = 8, d = 0 \).

Step2: Calculate the real part of the midpoint

Real part \(=\frac{a + c}{2}=\frac{8+8}{2}=\frac{16}{2} = 8\).

Step3: Calculate the imaginary part of the midpoint

Imaginary part \(=\frac{b + d}{2}=\frac{7 + 0}{2}=\frac{7}{2}=3.5\).

Answer:

\( 8 + 3.5i \)