Is this a variant of Euler's Formula? Understanding e^iy = cosy + isiny

Thread starter SpartanG345
Start date Mar 6, 2010
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Eulers formula Formula

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Euler's formula states that e^ix = cosx + isinx, and the variant e^ikx = coskx + isinkx is derived by substituting y = kx. This substitution maintains the fundamental relationship of Euler's formula while adjusting for the frequency factor k. The formula remains a valid application of Euler's principles, demonstrating how the exponential function can represent oscillatory behavior in a more generalized form. Understanding this transformation clarifies the connection between complex exponentials and trigonometric functions. The discussion emphasizes the consistency of Euler's formula across different contexts.

Mar 6, 2010

SpartanG345

Eulers formula says that e^ix = cosx + isinx

but in my textbook there's another formula its e^ikx = coskx + isinkx
i still can't figure out how they got that. Is this still eulers formula? and how do u get it in that form

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Mar 6, 2010

Feldoh

e^iy = cosy + isiny

Let y = kx

e^ikx = coskx + isinkx

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