Complex Numbers Circle Equation

[jsi]

Homework Statement

Write the equation of a circle in complex number notation: The circle through 1, i, and 0.

Homework Equations

The Attempt at a Solution

I know the equation for a circle with complex numbers is of the form |z-a| = r where a is the center point and r is the radius. I don't know how I'd go about finding it where they only give you 3 points like this. I assume the points correspond to complex numbers like w = x + iy == (x,y) so they'd be (1,0) (0,1) and (0,0)? I'm not sure where to go next and any help would be appreciated! thanks!

 

[Dick]

Homework Statement

Write the equation of a circle in complex number notation: The circle through 1, i, and 0.

Homework Equations

The Attempt at a Solution

I know the equation for a circle with complex numbers is of the form |z-a| = r where a is the center point and r is the radius. I don't know how I'd go about finding it where they only give you 3 points like this. I assume the points correspond to complex numbers like w = x + iy == (x,y) so they'd be (1,0) (0,1) and (0,0)? I'm not sure where to go next and any help would be appreciated! thanks!

Yes, think of the points (1,0), (0,1) and (0,0). Think of doing some geometry to find the center. E.g. the perpendicular bisector of each segment connecting two of those points goes through the center, right?

 

[jsi]

ok, so then would the center be at (1/2, 1/2)?

 

[jsi]

ok, I figured it out. Geometrically I found the center to be (1/2, 1/2) and then used that to find the radius from that point to a different point, (0,0), since that's easy to do then did sqrt((1/2)^2+(1/2)^2) to find the length of it which came out to 1/sqrt(2) so then the equation is just |z-(1/2)(1+i)| = 1/sqrt(2). Thanks for your help!