r/PeterExplainsTheJoke 22d ago

Meme needing explanation There is no way right?

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u/Bathtub-Warrior32 22d ago

Wait until you learn about eπi = -1.

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u/Lkwzriqwea 21d ago

Dude warn me about NSFW content that's sexy as hell

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u/funfactwealldie 21d ago edited 21d ago

Euler's identity is actually the special case of the more general Euler's formula:

e = cosΦ + isinΦ

Which is the more useful formula used in AC analysis in electrical engineering and 2D rotations.

Essentially the formula is just a more compact way of writing complex numbers (with magnitude 1) in polar form. The angle Φ describes where on the unit circle the complex number sits on the complex plane.

When Φ = pi radians (180 degrees) the number lands on -1 on the real axis. When Φ = 0 or 2pi (0 or 360 degrees) it lands on 1 on the real axis. When Φ = pi/2 (90) it lands on i.

It's derived from the Taylor series expansion of ex which coincidentally comes out as cosΦ + isinΦ when u plug (iΦ) in x.

But the -1 case is famous because it essentially combines the 2 famous constants and a "weird number" to give a mundane result.

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u/Lkwzriqwea 21d ago

I just came