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I'm currently writing a report on quantum entanglement however getting a little confused with some of the concepts.

If anyone could help with the following it would be greatly appreciated.

I know that an electron has a spin; which means that is has both an electric field and a magnetic field. In otherwords, it has an electric field (an arrow) that is also rotating (with the arrow the axis of rotation). This means electron spin is described by a complex vector - a vector because its an arrow, a complex vector because its also rotating and therefore has a phase. But I know its not possible to add the spins of two electrons together, and instead you need to take a tensor product, but I'm sure sure as to why you can't add the two spins together.

Can anyone help?