How to save an image with the Python Image Library

I am a beginner in Python, so this question might be stupid but unfortunatly I can't figure it out on my own.

With the following script I want to create a black image and save it under the following path: C://Users/User/Desktop/black.png

def create_file(x=1000,y=10):
    img = Image.new('RGB', (x,y), "black") #creates a new black image
    img.save('C://Users/User/Desktop/black.png')`

The point is now that I want to pretend the path, the filename and the filetyp with the function like that:

create_image(x=1000,y=10,path=C://Users/bsimon/Desktop/,filename=black,filetype=png)`

And there the struggle begins:

1. 
   

   I cant find the exact Syntax how I can deliver the path (filename, filetyp) to the img.save function

   
   


2. 
   

   I got errors by using a different filetyp than png. The line img.save('C://Users/User/Desktop/black.png') works fine but when I try to use img.save('C://Users/User/Desktop/black.bmp') instead for example, the program I run the script with (Blender) crashes or get stucked in an endless loop).