Match Pattern for example.com.*

Question

I am making a chrome extension and I have am having difficulty finding out how to make my content.js run on the pages I want.

My manifest.json have this:

"content_scripts": [{
    "js": ["content.js"],
    "matches": ["https://www.example.com/*"]
}]

Now I know this will allow https://www.example.com/(any_path) to run the content.js, however, I am trying to make it so that it will run on https://www.example.com.*, for instance I want the extension to work on https://www.example.com.au and https://www.example.com.uk etc. Is there anyway to do this?

I have tried doing this in my manifest.js, but it doesn't seem to work:

"content_scripts": [{
    "js": ["content.js"],
    "matches": ["https://www.example.com.*"]
}]

Any suggestions are appreciated.

Thanks