Real and Imaginary Numbers

Tan Tom

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Joined
Feb 19, 2019
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2
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.5pin) +a_3 e ^ -(j.5pin) + 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]
 
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