Find each of the following limits:

(1) $\lim_{z \to 2+5 i}{(z\ -\ 7 i)^2}\ =\ $

(2) $\lim_{z \to 2 i}{\frac{z^2\ +\ 4}{z\ -\ 2 i}}\ =\ $

(3) $\lim_{\Delta z \to 0}{\frac{(z_0\ +\ \Delta z)^2\ -\ z_0^2}{\Delta z }}\ =\ $ (Hint: You may use $z_0$ in your answer, simply write it as $z$.)