Sum over random number?

Questions
1

Total[Table[E^(I 2 [Pi] RandomReal[]), 10000]]

Hi,
I wrote this code to generate a series of complex number, e^i2??, and ? is between 0 to 1. Then, I sum them up. I expect the result should be very close to zero, but the value calculation giving me is a little large around ± 100.

Is my idea wrong?

Thanks

2

You can think of it as doing a random walk in the complex plane with unit steps and random directions every step. Doesn’t mean you always end up where you started.

3

Hello,

this is the Mean, not the total, which should convege to zero (Weyl’s criterion).

Claude

4

This is a good point of view. Thx.

5

You are right. My series is not converged. I know where the problem is now.