OK. Well, I don't think you need anything in the destructor, but can you work out why? operator<< should be easy enough, you just need to output (real,imag) and work out what to return so that multiple << operators can be chained (hint: look at the existing operator>>).

operator >> ( istream &in_file, complx &number ) will I imagine be more or less identical to operator >> ( ifstream &in_file, complx &number ) although you should check if any of the istream operators used differ from the equivalent ifstream operators: if not, then you can more or less lift the code directly.

What do you think operator== should do, based on the name? (This question assumes you know what == does.) Can you work out how to achieve that, and what to return? Look at the return type for a hint, and think of what values might be appropriate in what circumstances.