Question

A circle has a diameter with endpoint at 5 + 18i and -3 + 2i. What is the center of the circle?

Answer 1

so there is a real and imaginary axis
the midopint is just the average of them
average between the reals is (5-3)/2=2/2=1
average between imaginaries is (18i+2i)/2=20i/2=10i

center is 1+10i

Answer 2

center of the circle is 1+10i

Explanation:

The end points of the diameter are 5 + 18i and -3 + 2i.

We know that the center of the circle is the mid point of the diameter.

Thus, in order to find the center of the circle we find the mid point of the diameter.

The mid point of the diameter with endpoints 5 + 18i and -3 + 2i is given by

`\text{Center}=(5-3)/(2)+(18i+2i)/(2)\\\\\text{Center}=1+10i`

Thus, the center of the circle is 1+10i