Modulus of a Complex Number Question

[tylerc1991]

Homework Statement

My prof was saying today that the modulus of a complex number isn't the absolute value. The problem is the following:

Graph the set of points satisfying the following equation(s):

|z-1+i|=1

The Attempt at a Solution

Can I not just say that z = -i or z = 2-i and hence the graph is just two points? Or is this the correct answer?

 

[rock.freak667]

If you plot |z-1+i|=1 on an argand digram, you will see that this does not give only two solutions. If you put z=x+iy into the equation and then find the modulus knowing that |a+ib|=√(a²+b²), what do you get?

 

[tylerc1991]

I see what I did wrong now. If I let z = x + iy I am getting:

(x-1)^2 + (y+1)^2 = 1, which is obviously a circle.

Thanks!