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Euler’s Formula

Right. Just installed MathML block for WordPress because I want to talk about Fourier Series.

I’m just going to write a quick sidetrack required for the next post (and also for testing the MathML block).

Here’s the Euler’s formula discovered in 1748.

eix=cos(x)+isin(x)

This can be visualized as a unit complex number that rotates clockwise around the origin on the complex plane for every increase in x.

We can reverse the direction of the rotation simply by doing:

eix=cos(x)isin(x)

With this, we can easily represent any cosine as:

cos(x)=12(eix+eix)

Likewise, sines can be represented as such too:

sin(x)=12j(eixeix)

By Kelvin Ang

Ang Kah Min, Kelvin Singapore NUS Computer Engineering Shopee Engineering Infra Marketplace SRE

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