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Is $\delta\left(a+bi\right)=\delta\left(a-bi\right)$? I wonder whether Dirac Delta (as defined via Fourier transform) is symmetric against the real axis. We can write Delta function as $$\delta(z) = \...

$$f(\omega,u):=\frac1{\omega+iu}$$ where $i$ is the imaginary unit number. We see that the integral of a Fourier transform $$\int_1^\infty du\int_{-\infty}^\infty d\omega\,f(\omega,u)\,e^{-i\omega x}=...