two fan noises 92 e32

I am experiencing two fan noises (Just purchased car).

One; if I turn the key on (but dont' start the engine) I hear a fan like noise
from the engine. I also hear this noise more loudly when I turn the car off
(after running the engine).

Both fan-like noises are definately coming from the engine area (not interior).

The louder of the two is when I turn teh car off - it's like it's sighing "Ohhh
you're done.."

Are these noises normal?

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