Complex Numbers

Question

|Z-1| <= |Z-i| and |z-2-2i|<= 1. Sketch the region in the argand Diagram which contains the point P representing z. If P describes the boundary of this region, find the value of z. If P describes the boundary of this region, find the value of z when arg(z-1) = π/4

Answer 1

If you simplify the first inequality, |Z-1| <= |Z-i|, you get: y<=x, where x=Re{z), y=Im(z).

|z-2-2i|<=1, represents a circle of the radius 1 with the center in the point (2, 2). Now the whole region is intersection of both sets. (Draw and see it).

 

Now, arg(z-1)= π/4 for all z∈C such that

{Re(z) > 1 and  Im(z) = Re(z)-1}. 

 

I know that the answer is incomplete because the question is not stated well. I hope this answer will help you somehow.But you feel free to message me if any questions.