I need help with the following problem:

Let Fk = [ 1, 1, -j, 0, 0, 0, j, -j, 1, 0] which is the DFT of f[n]

Determine f[n]

I'm using the equation f[n] = (1/2pi) * int(0 to 2pi) {FK * exp(j*omega*n d(omega)}

I keep getting zero for each value. I'm pretty sure that's wrong. Is this equation correct? If not, what equation should I use? Any help would be appreciated.

Is the inverse of 1 2pi * dirac[n]?

What is the inverse of j? -j?

Thanks