Im: (z+i)/(1-z) = 1

|z|=1

What i did so far:

im: (a+bi+i)(1-a+bi)/(1-a-bi)(1-a+bi)=1

im: (a-b-(a^2)-(b^2)-ai+bi+i)/((a^2)+(b^2)-2a+1)=1

-a+b+1=(a^2)+(b^2)-2a+1

(a^2)+(b^2)-a-b=0

From here on forward i'm not sure how to proceed because i don't know how to implement the |z|=1 in the equation.What i did is this but i'm fairly certain it's not correct:

(a-(1/2))^2+((b-(1/2))^2 - 1/2 = 0

(a-(1/2))^2+((b-(1/2))^2 = (sqr.root 2/2)^2

My assumption for the solution is: all points on radius of (sqr.root 2/2)^2 with center at (1/2,1/2)

Would appreciate your help. Thank you