A straight line $T$ passes through $p=\sqrt{3}-2+3i$ and is a tangent to $S$, where $S$ is defined by $S=\left\{ z:\; \left| z+2-2i \right|=2,\; z\in C \right\}$. $T$ can be defined by $T=\left\{ z:\; \left| z+2-2i \right|=\left| z-d \right|,\; z\in C \right\}$. Find the complex number $d$.
Circle $S$ has an equation of $\left( x+2 \right)^{2}+\left( y-2 \right)^{2}=4$ and I can verify that $p$ is on $S$ by substituting $\mbox{Re}\left( p \right)$ and $\mbox{Im}\left( p \right)$.
I sketched the Argand diagram on paper, but here's the accurate diagram ($p$ is the blue dot):
Now $T$ is tangent at $\left( \sqrt{3}-2,3 \right)$, and I can get $\left| z-d \right|=2$, but that's all I could manage.
How can I find $d$?