Ak5hayPathak/ComplexLibrary ? reverse-engineered prompt

Build me a simple Java library for working with complex numbers.

I want it to make it easy to create complex values, do the basic math on them, and print them in a clean readable way. Please include the usual operations like add, subtract, multiply, divide, conjugate, magnitude, and maybe a way to compare values sensibly. It would be nice if the library also handles parsing a complex number from a string and gives helpful errors when the input is bad.

Please keep it straightforward and easy to use from other Java code, with a small example showing how to use it. If it helps, add a few tests so I can see it works as expected. Use current Java best practices, and if you need to check anything, look up the latest docs online.