Chapter One: The Prohibition of Killing a Non-Jew

In this chapter we deal with the notion that the prohibition of 'don't murder' doesn't apply in the context of a non-Jew. And, the prohibition of Jews killing non-Jews is learned from the prohibition given to the offspring of Noah against killing others. In the appendixes of the chapter we deal with another principle that the Jews are obligated in the commandments given to Noah.

Point 1. Shedding Blood Amongst Non-Jews
One of the seven commandments given to the offspring of Noah is the prohibition against shedding blood. In chapter 9 of the Laws for a King the Rambam says:

[1]Adam was commanded six things: not to engage in idolatry, praising God, no shedding blood, no immodesty, no theft, and establishing a court... another commandment was added for Noah, and that is not eating the limb of a live animal... [10] a non-Jew that kills another person, even a fetus in his mother, he will be killed

The words of the Rambam deal with a non-Jew who kills a non-Jew. So, here we will clarify the law that deals with a Jew who kills a non-Jew. Is such an act forbidden, and if so what is the extent of the prohibition?