Question

a circle has a diameter with endpoints at -2 + i and -6 - 11i. what is the center of the circle?
-8 - 10i
-4 - 5i
-2 - 6i
2 + i

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 $z_1$ and $z_2$

Let $z_1=-2 + i$ and $z_2=-6-11i$.

Step3: Calculate the real part of the mid - point

The real part of the mid - point is $\frac{-2+( - 6)}{2}=\frac{-2-6}{2}=\frac{-8}{2}=-4$.

Step4: Calculate the imaginary part of the mid - point

The imaginary part of the mid - point is $\frac{1+( - 11)}{2}=\frac{1 - 11}{2}=\frac{-10}{2}=-5$.
So the center of the circle (mid - point of the diameter) is $-4-5i$.

Answer:

B. $-4 - 5i$