$$\int dz_{1}^{*} dz_{1}\exp\Bigg[-z_{1}^{*}z_{1}+z_{1}^{*}z_{0}-az_{1}^{*}z_{0}-z_{2}^{*}z_{2}+z_{2}^{*}z_{1}-az_{2}^{*}z_{1}\Bigg]$$ where $z_{1}^{*}$, $z_{1}$, $z_{2}^{*}$, $z_{2}$, $z_{0}$ are complex numbers and $a\in \mathbb R$. Here $*$ does mean that it is complex conjugate and the integration is over $z_{1}^{*}$ and $z_{1}$ and rest of them are either complex constants are real constants.
I have rearranged this integral to make it more easier as follows,$$\int dz_{1}^{*} dz_{1}\exp\Bigg[-z_{1}^{*}z_{1}+z_{1}^{*}(z_{0}-a)z_{0}-z_{2}^{*}z_{2}+z_{2}^{*}(z_{1}-a)z_{1}\Bigg]$$ Again,$z_{2}^{*}z_{2}$ is just constant so I can just pull it out of the integral. so the integral becomes,$$\exp\Bigg[-z_{2}^{*}z_{2}\Bigg]\int dz_{1}^{*} dz_{1}\exp\Bigg[-z_{1}^{*}z_{1}+z_{1}^{*}(z_{0}-a)z_{0}+z_{2}^{*}(z_{1}-a)z_{1}\Bigg]$$ How do I proceed further to complete the integral ?