Exploring Complex Wave Equations: From (8) to (9)

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SUMMARY

The discussion focuses on the transition from equation (8) to equation (9) in complex wave equations, emphasizing the convention of expressing waves as complex exponentials. The imaginary part, represented by isin(omega*t-kz+phi), is often ignored for simplicity, although it plays a crucial role in fields like Quantum Mechanics. The use of complex forms facilitates easier mathematical operations compared to traditional trigonometric identities.

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From equation (8) to equation (9) fro the link attached below which the equation is written into a complex form. But why can it be written in that form even though the equation do not have an imaginary part isin(omega*t-kz+phi)?

http://scienceworld.wolfram.com/physics/WaveEquation.html
 
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Good question :smile:

It's a matter of convention, we usually just ignore the imaginary part (note that this is not always the case though, for instance in Quantum Mechanics we often need the imaginary part as well). The reason waves are usually expressed as complex exponentials is that it makes the math easier (believe it or not), it's a lot easier to perform various additions, multiplications, etc. with an exponential than it is to try and slough through trig identities.
 

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