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Subject: Re: Question to Euler.
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Date: Mon, 26 May 25 20:56:17 +0000
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From: Python <jp@python.invalid>

Le 26/05/2025 à 22:30, Richard Hachel a écrit :
> Z=r(cosθ+i.sinθ), I understand.

Are you sure of that? I doubt it.

> Z=e^iθ, I don't understand the expansion.

No doubt about that. What you wrote is incorrect, the correct expression 
is Z = r*e^(iθ)

Nice that you asked though.

> Does anyone understand?

Sure.

sin(x) = sum_(k=0)^\infty ((-1)^k x^(1 + 2 k))/((1 + 2 k)!)

cos(x) = sum_(k=0)^\infty ((-1)^k x^(2 k))/((2 k)!)

e^x = sum_(k=0)^∞ x^k/(k!)

i^2 = -1

Hence:

e^(ix) = cos(x) + i*sin(x)