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## Homework Statement

Let S = {z : 1<= Im(z) <=2}. Determine f(S) if f: S ->C

defined by

f(z) = (z + 1) / (z - 1)

## Homework Equations

z = x + iy

## The Attempt at a Solution

[attempt at solution]

so here my solution

f(z) = 1 + 2/(z - 1)

after doing some algebra <-> f(z) = x^2 + y^2/((x - 1)^2 + y^2) - [2y/((x-1)^2 + y^2)]i

therefore Im(z) = -2y/((x - 1)^2 + y^2) so F(S) = {z : 1<= (-2y)/((x-1)^2 + y^2) <= 2}

but I am stuck at this point I don't know wat does this represent.