[SOLVED] Convergence of a series

I have a question that I can't do...can anybody help me?

Investigate the convergence of the series (in the complex plane) for difference values of a and b:

Generalise your solution by determining what constraints are required on the values of a and b, so as to guarantee the convergence of the series?

$\displaystyle S(a,b) = \sum_{n=0}^{\infty}(a+bi)^n $

Thanks if you can help.

Sorry, still trying to understand

But I thought a + bi is a complex number.

i.e. b is not real.

so b could be a complex number?

So the assumption was that a and b are real numbers i.e.

it is not of the form a + (c +di)i

that's what I now understand of that that assumption is assuming.

Is this correct?

you're right, that was a stupid question.