Gonna is a short form of going to.
That sounds a little bit like slang. Is it common to use it in written English and even in business English?
"Gonna" is an informal contraction of "going to". It's used in informal speech.
While informal writing is, well, informal (and thus the rules are loosely defined), I've never seen "gonna" in writing, except in SMSspeak. And, of course, in written dialogues in novels/etc.
So, while there's nothing stopping you from using it wherever you want, I suggest you only use it in informal writing if you want to have it in a dialogue. Never use it in formal English.
Gonna is informal; you can use it in written English, but it is not normally used in business English.
Never in writing, unless you are writing dialogue in a novel. And never in a job application! It is slang, use it in informal speech, text messages, only with people you know.