Why doesn't a photon lose energy according to $E=mc^2$?

Question

As photons are massless thus by $E=mc^2$, the energy should be zero right? or should it be? I would be pleased to be corrected

Answer 1

The full formula is $E= \sqrt{c^2p^2+m^2 c^4}$, so for massless particles $E= pc$. The momentum $p$ of of photon is given by $p= h/\lambda$, so, from $\lambda \nu=c$ where $\nu$ is the frequency, we have $E= h\nu$ .