Let $z\ =\ -3+i$. Calculate the following:

(a) $z^2\ +\ 2z+ 1\ =$ $+$ $i$,

(b) $z^2\ +\ iz\ -\ (-3\ +\ i)\ =$ $+$ $i$,

(c) $\displaystyle \frac{(z\ -\ 4)^2}{z\ +\ i}\ =$ $+$ $i$.