/sci/ - Science & Math

>>12346448
[math](-1)^{1.7}= e^{1.7\cdot ln(-1)}[/math]
[math]ln(-1) = \pi \cdot i[/math] Use taylor expansion of e and plug in pi*i if you dont believe it.

Using a result from euler which he proved by lookin at taylor expansions we know.

[math]e^{ix} = cos(x)+i\cdot sin(x) \hspace{3em} \forall x \in \mathbb{R} \\ \therefore e^{1.7\cdot ln(-1)} = cos(1.7)+i\cdot sin(1.7) [/math]
using a finite taylor series we can approximate the result as
[math]cos(1.7)+i\cdot sin(1.7)\approx 0.587785252 - 0.809016994 i[/math]