# What is the physical significane of Complex Time Evolution in EM Waves? [duplicate]

So, I have been having a hard time understanding why there is even a complex phase for EM waves:

$$\phi=\exp[i\omega t]=\cos(\omega t)+i\sin(\omega t)$$

Don't understand why it is there? Any one have an explanation?

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## marked as duplicate by Brandon Enright, tpg2114, John Rennie, jinawee, Emilio PisantyMar 3 '14 at 11:17

@user1886681 Try expanding $\left(cos (\omega t) + i sin (\omega t)\right)\left(cos (\omega t) - i sin (\omega t)\right)$. –  EtaZetaTheta Mar 3 '14 at 4:33