$-$r Let $f$ be a Function defued in some neighbourhood of $Z_0$ with the possible exception of the point $z_0$ itself. We say that the limit of $f(z)$ as $z$ approaches $z_0$ is the Number ${}_0$ and ${}_{\text{r}\text{i}\text{t}\text{e}}$:$\underset{zt}{lim}f(z)={}_0.$ Hence $|f(z)-{}_0|<mi></mi>$ whenener Use the definition above to prove that

$\underset{zi}{lim}{z}^2=-1$

$\underset{z{z}_0}{lim}f(z)={}_0$

We must show that for a quen $>0$ there is a pariture number $$ such that:$-$

$z^2=f(z)$

$-1={}_0$

$|f(z)-{}_0|<mi></mi>$ whenener $|z-z_0|<mi></mi>$

$|z-i|<mi></mi>$

$|z^2+1|<mi></mi><mi>|</mi><mi>|</mi><mi>|</mi>$

$|(z-i)(z+i)|<mi></mi>$