How can i get exponential distribution form complex gaussian distribution?

Hi, I am currently trying to calculate exponential distribution form complex gaussian distribution

and complex gaussian distribution folloing(0,a)

Basically exponential distribution can drivation form complex gaussian distribution with(0,1)

So I just substituted x/a into the exponential distribution pdf

Because it is possible to normalize using z = (x-m) /s

And I got a meaningful result but not sure if this is correct

I searched on Google and couldn't get the answer I wanted.

Any helpful webpages or tips would be appreciated.