Geometric Sum, involving complex numbers

Hi Forum!

I came across an exercise involving both geometric sum and complex numbers.

I've read through Wikipedia and found: The summation formula for geometric series remains valid even when the common ratio is a complex number.

So, for the question:

A sequence has ten terms with first term $\displaystyle i$, for$\displaystyle i = \sqrt-1$. Each subsequent term is 2i times its previous term. That is, the 2nd term is $\displaystyle i.2i $ .

The sum of this sequence is a + bi . What is the value of |a + b|?

If we wish to get the sum of the geometric progression we use:

$\displaystyle S_n=a(1-r^n)/(1-r)$

Using this you only give headaches, since we are searching for a+bi solution.

So, what would be the best approach? --besides from calculating all the terms up to n=10.

Is it really possible to use the geometric sum formula here?

Thanks!