When Euler discovered/invented $e^{ix} = \cos(x)+i\sin(x)$. Did he doubt his calculations for a length of time? Was it Readily accepted by the mathematical community quickly or did they object at first? If so when was it finally accepted and why?
2026-04-05 23:42:15.1775432535
Eulers identity history
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Work with power series was innovated by James Gregory and Isaac Newton almost a century earlier so the kind of arguments Euler presented in his 1748 Introductio were easily digestible by his contemporary mathematicians. The Introductio is full of calculations with power series a lot more complicated than the one you mentioned. I have seen no evidence that anybody doubted Euler's formula. His infinite product formula for the sine function was far more innovative; that also seems to have elicited no objections. For a detailed study of the formula see for example this acticle.