In this paper, the authors rigorously analyze the optimal input distribution and capacity of an additive Bernoulli-Gaussian (BG) Impulsive Noise (IN) channel in high and low input power regimes. First, they obtain an input distribution for which the channel output is Gaussian distributed. This distribution, if valid, shall result in the capacity of the channel. At an asymptotically high input power level, they then show that the derived input is always valid and in fact, it resembles a Gaussian distribution. As such, the Gaussian channel input is considered approximately optimal. Using the monotonicity property of the Characteristic Function (CF), they then develop a necessary condition for the existence of the derived optimal input for a finite level of input power.