I have seen one of my language partners use 牛气 and 很牛, but he couldn't explain it to me. The context suggested it meant something like "bullshit" or "you are kidding me", a sign or disbelief, but the dictionaries I tried only suggested literal cattle-related translations. Do they have another meaning?
Most likely, 牛氣 and 很牛 came from a slang '牛逼' (cow's genital)
Cow's genitals are huge compare to human's. Calling something 牛逼 means it is unbelievably impressive or out of worldly awesome.
- 牛氣 (emitting aurar of unbelievable impressiveness)
- 很牛 short for 很牛逼 (very unbelievably awesome) * this example showed 牛逼 can be simplified to just 牛
There is a common term 牛脾氣(temperament of a bull), which means " hot tempered" or "extremely stubborn" . But I don't think it is related to the term '牛氣' we are discussing here, because 牛脾氣 is not usually shortened.
I previously stated 牛逼 meant bull's penis, but it should be cow's genital instead. (I remembered it wrong, May be I thought it make more sense to be impressed by a male genital than a female genital.) Aside from this difference, the answer remain the same -- 牛氣 and 很牛 came from a slang '牛逼'
"气" is a suffix which turns an adjective to a noun. But nouns ending with it often describe a quality that may offend people, called "咄咄逼人" in Chinese.