Line 10: is a copy constructor.
const
is used for the argument since the copy constructor does not change the argument.
For the following lines, I am presuming what the functions do from their names since the class declaration is not documented.
Line 15: Returns the conjugate of a complex number.
https://en.wikipedia.org/wiki/Complex_conjugate
Line 16: Returns a complex number that is the reciprocal of a complex number.
Line 17: Returns a modulus (absolute value) of a complex number.
Line 18: Sets the real and imaginary parts of a complex number.
Line 19: No idea what this does. Perhaps it prompts the user to enter the real and imaginary parts of a complex number.
Line 20: Returns the real portion of a complex number.
Line 21: Returns the imaginary part of a complex number.
Line 22: Compares 2 complex numbers.
Line 23: Assigns one complex number to another.
Line 24: Formats a complex number to an output stream.