To prove that the limit as p appraoches infinity of i^(p) you can use Eulers rule.
Recall that the $$\lim\limits_{n \rightarrow \infty} (1 + \frac{x}{n})^n = e^x $$
By definition you also know that $$(1+i) = (1+\frac{i^(p)}{p})^p$$
therefore $$\lim\limits_{n \rightarrow \infty} (1 + \frac{i^(p)}{p})^p = e^{i(\infty)}$$
and so $$ i^{\infty} = \delta$$