- #1

alexcc11

- 21

- 0

## Homework Statement

Sketch the following regions and state the interior and the closure:

a) |z-2+i|≤1

b) Im(z)>1

## Homework Equations

z=x+iy

## The Attempt at a Solution

a) z=x+iy so |x+iy-2+i|-> |(x-2)+i(y+1)|≤1

So (x-2)

^{2}+(y+1)

^{2}≤1

So it would just be a circle on the real plane? And the interior would be the equation with < instead of ≤ right? I'm not sure how to write the closure though.

b)Im(z)= y so it would be a straight line at y=1 on the real plane and there is no interior or closure since it is an open set right?