Question

What is the length of the radius of a circle with a center at 2 + 3i and a point on the circle at 7 + 2i?

Answer 1

You can calculate the difference/vector of both points:
$7+2i-(2+3i)=5-i$
then calculate the magnitude/length like pythagoras
$radius=\sqrt{5^2+(-i*-i)}\\=\sqrt{5^2+i^2}\\=\sqrt{5^2-1}\\=\sqrt{24}\\=\sqrt{4*6}\\=2*\sqrt{6}$

Answer 2

Answer:

Hence, the length of radius is:

$\sqrt{26}$ units.

Step-by-step explanation:

The center of circle is at: 2+3i.

Hence, the coordinate of the center is: (2,3)

The point on the circle is: 7+2i

Hence, the coordinate of the point is: (7,2).

The radius of the circle is the distance between the center of the circle and the point on the circle.

We know that the distance between two points (a,b) and (c,d) is given by:

$\sqrt{(c-a)^2+(d-b)^2}$

We have (a,b)=(2,3) and (c,d)=(7,2).

Hence, the distance between the two points is:

$\sqrt{(7-2)^2+(2-3)^2}=\sqrt{(5)^2+(-1)^2}\\\\\\=\sqrt{25+1}\\\\=\sqrt{26}$

Hence, the length of radius is:

$\sqrt{26}$ units.