Rather than define extraneous variables I'd like to define only a subset of the indices of x in Ax=b as cp.Variable. It this possible? I've tried using numpy arrays like this but it does not work:

x = np.full(10, 0.0)
var_indices = [3,4]
var = cp.Variable(len(var_indices))
x[var_indices] = var

ValueError: setting an array element with a sequence.

Why would that be beneficial? And what would the other indices of x be?
I think you might mean defining variables that are sparse (i.e. only a subset of the entries are non-zero).
If so, please refer to the documentation here.

I ultimately ended up splitting the complex variables into real and imaginary variables so that I could use the sparsity option in a Variable. I would be nice if more than one Variable option were supported.