One of the attempts at combining the two sets of Hamilton’s equations into one tries to ta...

One of the attempts at combining the two sets of Hamilton’s equations into one tries to take q and p as forming a complex quantity. Show directly from Hamilton’s equations of motion that for a system of one degree of freedom the transformation

is not canonical if the Hamiltonian is left unaltered. Can you find another set of coordinates Q′, P′ that are related to Q, P by a change of scale only, and that are canonical?