I have a bit of a background in math, but not a professional one. I have been aware of Euler's Identity since my college years, perhaps even earlier, but have never seen a derivation or proof of it that satisfied my curiosity.

Euler's Identity: e^(i*pi) + 1 = 0

or e^(i*pi) = -1

At a first glance, the explanation is simple.

About 1/3 of the way down the page is an explanation that only requires high school algebra to understand. But it is based on what is called Euler's Formula which is more or less just another way of expressing Euler's Identity. So, that really is not a proof or explanation.

Euler's Formula: e^ix = cos x + i sin x

Now it gets a lot more dicey. The derivation of this formula is apparently based on Taylor series.

I am going to go through this page and others on the subject but that is going to take some time.

Does anyone have an easier way of understanding this? Mathematically? Perhaps a text or web page that shows the derivation in understandable steps?

Euler's Identity: e^(i*pi) + 1 = 0

or e^(i*pi) = -1

At a first glance, the explanation is simple.

About 1/3 of the way down the page is an explanation that only requires high school algebra to understand. But it is based on what is called Euler's Formula which is more or less just another way of expressing Euler's Identity. So, that really is not a proof or explanation.

Euler's Formula: e^ix = cos x + i sin x

Now it gets a lot more dicey. The derivation of this formula is apparently based on Taylor series.

I am going to go through this page and others on the subject but that is going to take some time.

Does anyone have an easier way of understanding this? Mathematically? Perhaps a text or web page that shows the derivation in understandable steps?

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