An analytical solution in the complex plane for the luminosity distance in flat cosmology

We present an analytical solution for the luminosity distance in spatially flat cosmology with pressureless matter and the cosmological constant. The complex analytical solution is made of a real part and a negligible imaginary part. The real part of the luminosity distance allows finding the two parameters $H_0$ and $\om$. A simple expression for the distance modulus for SNs of type Ia is reported in the framework of the minimax approximation.