Question

What is the length of the radius of a circle with a center at the origin and a point on the circle at 8 + 15i?

Answer 1

Answer: 17

Step-by-step explanation: the length of the radius of a circle with center at origin is 17 units.

Answer 2

Hence, the length of the radius of a circle with center at origin is 17 units.

Explanation:

" We know that radius of a circle is any line segment joining center to any point on the circle ".

We have to find the length of the radius of a circle with a center at the origin i.e. (0,0) and a point on the circle at 8 + 15i i.e. at (8,15).

( Since any complex number of the form z=x+iy has a point in the coordinate plane as: (x,y) ).

Hence , we have to find the distance between the point (0,0) and (8,15).

The distance between two points (a,b) and (c,d) is given by:

`√((a-c)^2+(b-d)^2)`

Here (a,b)=(0,0) and (c,d)=(8,15)

Hence distance between (0,0) and (8,15) is:

`√((0-8)^2+(0-15)^2\\) \\=√((8)^2+(15)^2\\) \\=√(64+225)\\ \\=√(289)\\ \\=17`

Hence, the length of the radius of a circle with center at origin is 17 units.