The question asks me to "use electron configurations to explain why copper is paramagnetic while its 1+ ion is not".
The question should have asked, Why is Cu?? paramagnetic while Cu? is not? Electron configurations: Cu??: [Ar]3d? - open shell, one of the 3d electrons is not paired with an electron with opposite spin Cu??: [Ar]3d?? - closed shell, no unpaired electrons Paramagnetic compounds must have unpaired electrons, hence the difference between Cu?? and Cu?. These comments pertain to isolated copper ions (complexes); bulk copper metal (Cu? - [Ar]3d??4s?) is not paramagnetic because its extra 4s electrons are paired in forming a sea of electrons that are responsible for the conductivity of the metal.
To define something as paramagnetic it must have a magnetic susceptibility greater than 0. Magnetic susceptibility is due to the the pairing of electrons in an atom. From the periodic table you can see that copper +1 is a d10 metal with all five d electron orbitals filled with both spin up and spin down electrons. Copper +2 has d9 electron configuration leading to an unpaired electron in one of the orbitals (which orbital usually will depend on the ligand). Since there is an unpaired electron the atom will exhibit a spin only moment and will be susceptible to an external magnetic field.