16. Let the complex number $z=x+i y(x, y \in \mathrm{R})$ satisfy $|z-i| \leqslant 1$, find the maximum and minimum values of $A=x\left(|z-i|^{2}-1\right)$ and the corresponding $z$ values.
16. Let $z-i=r(\cos \theta+i \sin \theta),|z-i|=r, 0 \leqslant r \leqslant 1$, then $x=r \cos \theta, A=r\left(r^{2}-\right.$ 1) $\cos \theta$. Therefore,
$A^{2} \leqslant r^{2}\left(r^{2}-1\right)^{2} \leqslant \frac{1}{2}\left[\frac{2 r^{2}+\left(r^{2}-1\right)+\left(r^{2}-1\right)}{3}\right]^{3}=\frac{4}{27}$, equality holds if and only if $r=$ $\frac{\sqrt{3}}{3}$, and $\cos \theta= \pm 1$, hence $-\frac{2 \sqrt{3}}{9} \leqslant A \leqslant \frac{2 \sqrt{3}}{9}$.
When $\cos \theta=-1$, $A>0, z=-\frac{\sqrt{3}}{3}+i, A$ reaches its maximum value of $\frac{2 \sqrt{3}}{9}$;
When $\cos \theta=1$, $A<0, z=\frac{\sqrt{3}}{3}+i, A$ reaches its minimum value of $-\frac{2 \sqrt{3}}{9}$.