Re: Question to Euler.

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)