Question

a circle has a diameter with endpoints at 3 - 5i and -8 + 2i. what is the center of the circle?
-5 - 3i
-\frac{5}{2}-\frac{3}{2}i
\frac{11}{2}-\frac{7}{2}i
11 - 7i

Explanation:

Step1: Recall mid - point formula for complex numbers

The mid - point of two complex numbers $z_1=a + bi$ and $z_2=c+di$ is given by $\frac{z_1 + z_2}{2}=\frac{(a + c)+(b + d)i}{2}$.

Step2: Identify the given complex numbers

Let $z_1=3-5i$ and $z_2=-8 + 2i$.

Step3: Calculate the real part of the mid - point

The real part of the mid - point is $\frac{3+( - 8)}{2}=\frac{3 - 8}{2}=-\frac{5}{2}$.

Step4: Calculate the imaginary part of the mid - point

The imaginary part of the mid - point is $\frac{-5 + 2}{2}=-\frac{3}{2}$.
So the center of the circle (mid - point of the diameter) is $-\frac{5}{2}-\frac{3}{2}i$.

Answer:

B. $-\frac{5}{2}-\frac{3}{2}i$