If an expectation value is purely imaginary, then the real component is obviously 0. Because expectation values are real quantities, does this mean that the expected value must be 0? I feel like this pretty self-explanatory but I want to be able to confidently put this on my assignment.
If an expectation value is imaginary, it means the expectation value is imaginary. An expectation value is just a statistical attribute of the distribution of observables.
Hermitian operators have real observables, in the form of real eigenvalues; and correspondingly the expected value of those operators must be real as well. Since every actual observable is real, all Quantum Operators which correspond to an observable are Hermitian, like Spin, Position, Momentum, ... , all the good stuff.
Now in your case, the fact that you get an imaginary E.V. means that there are imaginary eigenvalues to the operator. So the operator is not Hermitian. That's is fine and we can still calculate its E.V., mean, uncertainty...but the Operator does not correspond to a real life observable.