E-Powers Homework Help: Understanding Why e^[i(phi)] * e^[-i(phi)] = 1

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Homework Help Overview

The discussion revolves around the properties of exponential functions, specifically focusing on the expression e^[i(phi)] * e^[-i(phi)] and its evaluation. Participants are exploring the mathematical reasoning behind why this expression equals 1.

Discussion Character

  • Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions the equality of the expression, suggesting a potential misunderstanding of exponential properties. Another participant explains the rule for multiplying exponentials, indicating that the sum of the exponents leads to e^0.

Discussion Status

The discussion includes an explanation of the relevant mathematical property, and while there is acknowledgment of the explanation, the original poster's inquiry suggests a need for further clarification or exploration of the concept.

Contextual Notes

The original poster's question implies a possible confusion regarding the manipulation of exponents and their properties, which may reflect broader misunderstandings in the topic area.

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why does e^[i(phi)] * e^[-i(phi)]=1 instead of e^[(phi)^2]?
 
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Well for powers, so for e-powers in particular, we have that [itex]e^a \cdot e^b = e^{a + b}[/itex]. Applying that here gives e^0 which is of course 1.
 
thank you very much!
 
No problem :smile:
 

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