Infinite series of complex numbers.

[Nevermore]

I have the two series:
C = 1 + (1/3)cosx + (1/9)cos2x + (1/27)cos3x ... (1/3^n)cosnx
S = (1/3) sinx + (1/9)sin2x ... (1/3^n)sinnx

I have to express, in terms of x, the sum to infinity of these two series.

Here's what I've done so far:
Let z represent cosx + jsinx
C + jS = z^0 + (1/3)Z^1 ... (1/3)^n(Z^n)
This is a GP with first term 1, common ratio (1/3)Z.
Sum to infinity of C + jS = a/(1-r) = 3/(3-Z)

I can't seem to find where to go from there. Can anyone help?

Thankyou.

 

[CarlB]

Write z=x+iy and break your answer, 3/(3-z) into real and imaginary parts.

Carl