Understanding Wave Phase: A0cosϕ = ℜa0eiϕ

[mps]

The phase of a wave at (x,t) is a₀cosϕ = ℜa₀e^iϕ.

Where did this come from? I know that the phase of a wave is given by ϕ = kx−ωt+ϕ0 but then I am stuck.

Please help! Thanks :D

 

[tiny-tim]

hi mps!

The phase of a wave at (x,t) is a₀cosϕ = ℜa₀e^iϕ.

no, that's not the phase, it's the displacement (from x at time t)

the phase is ϕ = kx−ωt+ϕ₀ ​

 

[mps]

Thanks Tiny Tim! i totally get it now :)