+0 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!
