Continuous Time Fourier Series of cosine equation

[owtu]

Homework Statement

Using the CTFS table of transforms and the CTFS properties, find the CTFS harmonic function of the signal

2*cos(100*pi(t - 0.005))

T = 1/50

Homework Equations

To = fundamental period

T = mTo

cos(2*pi*k/To) ----F.S./mTo---- (1/2)(delta[k-m] + delta[k+m])

The Attempt at a Solution

using the table of pairs and CTFS properties, the solution I arrived to was:

1) Cx[k] = (delta[k - 1] + delta[k+1])*e^(-j*0.5*pi*k)

My solution is right but the final solution from the solution manual there's one more step to simplify it even more:

2) Cx[k] = j*(delta[k - 1] + delta[k+1])How did they go from (1) to (2) ?

 

[owtu]

Anyone?