stuck with root test for series convergence to $1$ for $\sum_{n=0}^{\infty} \left(\frac{(1+i)}{\sqrt{2}}\right)^n$ I've got this series and I used the series convergence root test.
However my problem is: The result of the root test is one, so I can't show wheter the series converges/diverges 
$$\sum_{n=0}^{\infty} \left(\frac{(1+i)}{\sqrt{2}}\right)^n$$
My approach 
$$ \sqrt[n]{\left|\left(\frac{(1+i)}{\sqrt{2}}\right)\right|^n}
= \left|\frac{1+i}{\sqrt{2}}\right| = \frac{\sqrt{2}}{\sqrt{2}}=1 $$
So, now I have 1 as result and can't decide wheter it converges or not?
Is there any other test I can use to show?

Actually it is a geometric series with ratio $\,\mathrm e^{\tfrac{\mathrm i\pi}4}$ and the general term is periodic, hence it cannot converge.
