You will need a base64 library and a zlib library. Make sure you decode the base64 data first, and then pass that into the zlib decoder. Note that the decompressed data is binary and should be interpreted as an array of integers, so you might still get garbage if you try to print it without interpreting it.
I’ve written about this in a bit more detail in my tip sheet.
Edit: Base64 and zlib libraries are available as header-only libraries, so you should be able to just drop those into your project without any linking difficulties.