Question

find the midpoint between 14 + 11i and 4 - 11i ? + 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, \( z_1 = 14+11i \) (so \( a = 14, b = 11 \)) and \( z_2=4 - 11i \) (so \( c = 4, d=- 11 \)).

Step2: Calculate the real part of the midpoint

The real part is \( \frac{a + c}{2}=\frac{14 + 4}{2}=\frac{18}{2}=9 \).

Step3: Calculate the imaginary part of the midpoint

The imaginary part is \( \frac{b + d}{2}=\frac{11+( - 11)}{2}=\frac{0}{2}=0 \).

Answer:

\( 9+0i \)