def remove_imaginary_terms(pauli_sums: PauliSum) -> PauliSum:
    """
    Remove the imaginary component of each term in a Pauli sum.

    :param pauli_sums: The Pauli sum to process.
    :return: a purely Hermitian Pauli sum.
    """
    if not isinstance(pauli_sums, PauliSum):
        raise TypeError("not a pauli sum. please give me one")
    new_term = sI(0) * 0.0
    for term in pauli_sums:
        new_term += term_with_coeff(term, term.coefficient.real)

    return new_term