Question

what is the length of the radius of a circle with a center at 2 - i and a point on the circle at 8 + 7i?
2√1
√10
8
10

Explanation:

Step1: Recall distance formula for complex numbers

The distance $d$ between two complex numbers $z_1=a + bi$ and $z_2=c+di$ is $d=\sqrt{(a - c)^2+(b - d)^2}$. Here, $z_1=2 - i$ (center) and $z_2=8 + 7i$ (point on circle), so $a = 2$, $b=-1$, $c = 8$, $d = 7$.

Step2: Calculate differences

$a - c=2-8=-6$ and $b - d=-1 - 7=-8$.

Step3: Apply distance formula

$d=\sqrt{(-6)^2+(-8)^2}=\sqrt{36 + 64}=\sqrt{100}=10$. Since the distance from the center of a circle to a point on the circle is the radius, the radius is 10.

Answer:

D. 10