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In section 1-3 An experiment with waves of The Feynman Lectures on Physics (https://www.feynmanlectures.caltech.edu/III_01.html) it says:

"The instantaneous height of the water wave at the detector for the wave from hole 1 can be written as (the real part of) ${h_1}e^{iωt}$, where the “amplitude” $h_1$ is, in general, a complex number."

What does it mean to have a amplitude that is a complex number? I'm used to working with the wave representation of $Ae^{iwt}$ where $A$ is just a constant describing the amplitude, so I'm a bit lost when this amplitude all of a sudden is a complex number.

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If $h= |h|e^{i\theta}$ then $he^{i\omega t}= |h|e^{i(\omega t +\theta)}$, so the phase is just shifted.

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    $\begingroup$ How does this answer the question? $\endgroup$ Dec 9, 2023 at 3:09
  • $\begingroup$ @MartinArgerami The complex part of the amplitude just encodes a phase shift $\endgroup$ Dec 9, 2023 at 19:12
  • $\begingroup$ @BioPhysicist: saying so in your answer would improve it a lot. $\endgroup$ Dec 9, 2023 at 23:15
  • $\begingroup$ @MartinArgerami Well, it's not my answer, but thanks! $\endgroup$ Dec 11, 2023 at 15:10
  • $\begingroup$ @BioPhysicist: my bad, I didn't notice it was not your answer. In any case, thanks for the clarification, which does answer the question for me. $\endgroup$ Dec 11, 2023 at 16:16

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