By considering the case when p = −1 separately find
$$\int_{c(0,1)}z^p dz$$
$c(0,1)$ means a circle around the origin of radius 1
where p ∈ $\mathbb{Z}$ and hence if n ∈ $\mathbb{N}$ ∪ {0} and $c_0,c_1,.........,c_{2n}∈ \mathbb{C} find$
$$\int_{c(0,1)}\frac{c_0+c_1z+.........+c_{2n}z^{2n}}{z^{n+1}}dz$$
so I evaluating at p=-1 to get the formula for every $z^{-1}$ which is $$\int_{c(0,1)} \frac{c_n}{z}dz$$
but I don't how how to take this any further or if this is even the right direction to go in. any help would be greatly appreciated.
This is good so far - now you just need to evaluate the last integral. Parametrize the contour as $\gamma(t) = e^{it}$, $t\in[0,2\pi)$ (assuming $c(0,1)$ is oriented counterclockwise), and use the usual definition of contour integration: $$ \int_\Gamma f(z)~dz = \int_a^b f(\gamma(t))\gamma'(t)~dt. $$