The set C of all complex numbers z satisfying (z+1)^{2}=a z for some a \in[-10,3] is the union of two curves intersecting at a single point in the complex plane. If the sum of the lengths of these two curves is \ell, find \lfloor\ell\rfloor.
The set C of all complex numbers z satisfying (z+1)^{2}=a z for some a \in[-10,3] is the union of two curves intersecting at a single point in the complex plane. If the sum of the lengths of these two curves is \ell, find \lfloor\ell\rfloor.