# Real and Imaginary Numbers

#### Tan Tom

Good morning,

I am working on a problem where I am finding the 4th Coefficient in a sample of 4 discrete time Fourier Series coefficients. I got the sum but now I have to solve for a_3 which consists of a real and imaginary part. Any assitance on how to solve for the a_3? Thank you.

a_k = {3, 1-2j, -1, ?}

Step 1: (1-2j)e^(j*.5pi*n) +a_3 e ^ -(j*.5pi*n) + 3 + (-1)^(n+1)

Step 2: [(1-2j)(cos (pi/2)n + j sin (pi/2)n) + a_3 (cos (pi/2)n)-j sin (pi/2)n]

#### skipjack

Forum Staff
What do you mean by "a sample"?