What is e^-iPi/2 and how can it be represented using cos and sin notation?

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Discussion Overview

The discussion revolves around the expression e^-iPi/2 and its representation using cosine and sine notation. Participants explore the relationship between complex exponentials and trigonometric functions, particularly in the context of complex numbers and their geometric interpretations.

Discussion Character

  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant asks for the value of e^-iPi/2 and its representation in cos + sin notation, referencing its appearance in an article on spinors.
  • Another participant states the formula e^(ix) = cos(x) + i*sin(x) for complex variable x.
  • A subsequent reply applies this formula to the specific case of x = -π/2, concluding that e^-iπ/2 = -i.
  • A participant expresses understanding of the concept, likening it to a geometric interpretation of rotating in the complex plane.

Areas of Agreement / Disagreement

Participants generally agree on the application of Euler's formula to the expression, but there is no explicit consensus on the broader implications or interpretations of the result.

Contextual Notes

The discussion does not address potential limitations or assumptions in the application of Euler's formula, nor does it explore the implications of the geometric interpretation in depth.

Who May Find This Useful

Readers interested in complex analysis, trigonometric identities, or the geometric interpretation of complex numbers may find this discussion relevant.

DiracPool
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If e^iPi/2=i, what does e^-iPi/2 equal? And could you please write it out in cos + sin notation? For some reason I am not geting this. This is not homework, by the way, its come up in an article on spinors I'm reading Thanks.
 
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A simple google check would do the trick.

Anywho, e^(ix)=cos(x)+i*sin(x) for complex variable x.
 
Klungo said:
A simple google check would do the trick.

Anywho, e^(ix)=cos(x)+i*sin(x) for complex variable x.

Continuing with this. If [itex]x=-\pi /2[/itex], then

[tex]e^{-i\pi /2}=\cos(-\pi/2)+i\sin(-\pi/2)=-i.[/tex]
 
I got the first one Klungo. Thanks for the follow up micromass. Now I got it, its just like spinning the dial from the top of the complex plane to the bottom.
 

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