Stuck on Complex Summations

[ed84c]

Right I'm revising my FP2 but I can't remember how in summations to find C or S seperately after you've found C + jS

I'll give an example;

 

Where C and S are Series'

 

C= cos(t)cos(t) + cos(2t)cos^2(t) + cos(3t)cos^3(t)...cos(n)cos^n(t)

S = sin(t)cos(t) + sin(2t)cos^2(t) + sin(3t)cos^3(t)...sin(n)cos^n(t)

 

(t is theta)

 

So I've proved these are geometric, and also the sum of C+jS which is

 

[math]

 

\frac{e^{j\theta}(1-(e^{j\theta}cos\theta)^n)}{1-e^{j\theta}cos\theta}

 

 

[/math]

I also know

 

[math]

1 - e^{j\theta}cos\theta = -je^{j\theta}sin\theta

[/math]

 

Any ideas as to find C and S would be very greatfully recieved

[sioprequi]

Try to use the trig/hyperbolic?