What are some practical examples of complex signals?
Here is one aspect that often creates confusion: In many cases, complex signals are used solely as a mathematical convenience, not because the complex representation is required by anything physical.
A good example is circuit analysis in electronics: all physical quantities (voltages, currents, impedances) are real and you can do the analysis with these quantities and the associated physical equations directly.
However, it's a lot easier if you convert the real quantities to complex ones, run the analysis in the complex domain and convert the results back to real. Hence, that's the way everyone does it.
So you don't HAVE to use complex signals, it just gets a lot easier if you do.