Please don't be angry
I'm confused with Duolingo's translation of "Please don't be angry" as "Bitte nicht böse sein." First, it seems like a polite imperative, so "Bitte sei nicht böse." Second, if its not an imperative, I would translate it as "Bitte böse nicht sein." What is the difference in meaning/connotation between Duolingo's "Bitte nicht böse sein" and my "Bitte böse nicht sein"?
(As a native speaker I'm a bit confused myself how those sentences work.)
"Bitte nicht" is the German equivalent of "Please don't". It basicly allows you to ask someone not to do something.
Please don't be angry! ► Bitte nicht böse sein!
Please don't forget! ► Bitte nicht vergessen!
Don't move! ►Nicht bewegen!
Do not disturb! ► Bitte nicht stören!
The verb isn't in imperative form, which makes those sentences sound impersonal or like they originate from an authority. So you can give commands in an authoritarian way by leaving the verb in infinitve form and kicking it to the end of the sentence. Nicht will be the first word in those sentences (with an exception for bitte) - which explains why your "Bitte böse nicht sein" isn't correct.
Please move on! ► Bitte geh weiter! ► (Bitte) Weitergehen!
Don't touch! ► Fass das nicht an! ► Nicht anfassen!
The first version sounds more personal and polite, the second sounds more like you adress a group of people or give a general directive.
While researching I found this site, which explains a lot about imperatives. I thought it could be useful and wanted to share it.
Just adding that, to me, "Bitte nicht böse sein" would sound more polite than "Bitte sei nicht böse". I think it's what a shy person would prefer to say, and/or somebody who feels uncomfortable about making that person angry (or sad, actually) (because of bad conscience, or because that person is a choleric), e.g. "Bitte nicht böse sein... I didn't see your red underpants in the laundry, and it turned your favourite shirt pink...", or, "...I can't come to that dinner with you tonight, I've got to work late at the office"
Actually, "Bitte böse nicht sein" has the wrong word order. Your version puts the predicate at the very end, which in German is always at the first or second position within your sentence. Since the predicate is a negative (do not be) it is split into "nicht" and "sein"; the "nicht" functions as part of the predicate and should come second.