HELP ASAPPPP!

1. What is the imaginary part of the center of the circle with the equation $\frac{|z-i|}{|z-1|}=3?$

2. Find the value of $d$ if the Mobius transformation $M(z)=\dfrac{4z+3}{z+d}$ is its own inverse.

3. The function $f(z) = \frac{(-1 + i \sqrt{3}) z + (-2 \sqrt{3} - 18i)}{2}$ represents a rotation around some complex number $c$. Find $c$.

Please include explanations so i can understand them, thanks!