Limit in complex analysis Can someone help me to solve these two questions:
$$\mathop {\lim }\limits_{z \to 1} {1 \over {{z^2} - 1}}$$
$$\mathop {\lim }\limits_{z \to 1} {1 \over {{{(z - 1)}^3}}}$$
I don't know how to solve it because when I substitute the answer is undefined.

When you plug $z=1$ into the denominators of each of these fractions you get $0$.  Further, the denominators are polynomials, and all polynomials are continuous, so when you plug in a value of $z$ close to $1$ then the denominators will be close to zero.
What happens when you take the reciprocal of something very small (something very close to zero)?  The reciprocal of something very small is something very large.
As $z$ gets closer and closer to $1$, the denominators get closer and closer to $0$, and their reciprocals get larger and larger.  In the limit as $z \to 1$, the denominators reach $0$, so their reciprocals reach $\infty$.  Because we're dealing with complex numbers, this infinity is called complex infinity.
