I am having trouble simplifying the following equations which are the solutions to the equation $\displaystyle (z+1)^5=z^5$.

$\displaystyle \frac{1}{e^{i\frac{2}{5}\pi}-1}$

$\displaystyle \frac{1}{e^{i\frac{4}{5}\pi}-1}$

$\displaystyle \frac{1}{e^{i\frac{6}{5}\pi}-1}$

$\displaystyle \frac{1}{e^{i\frac{8}{5}\pi}-1}$

Any help you can give me will be greatly appreciated!