- #1
NotASmurf
- 150
- 2
Hey all, I need the complex version of the sigmoid function in standard form, that is to say $$f(\alpha) =\frac{1}{1+e^{-\alpha}} , \hspace{2mm}\alpha = a+bi , \hspace{2mm} \mathbb{C} \to \mathbb{C}$$ in the simplified form: $$f = m+ni$$ but found this challenging, for some reason i assumed there was an identity for $$e^{e^{x} }, \hspace{2mm} x \in \mathbb{C}$$, so wasted my time with
$$e^{-a-bi}= e^{e^{tan^{-1}\frac{b}{a}i + ln[\sqrt{ a^{2} + b^{2} }]}}$$ and tried from there, (just showing I did make an attempt, no matter how abysmal). Any help appreciated as I am not too familiar with complex numbers outside of the basics needed for transformation matrices.
$$e^{-a-bi}= e^{e^{tan^{-1}\frac{b}{a}i + ln[\sqrt{ a^{2} + b^{2} }]}}$$ and tried from there, (just showing I did make an attempt, no matter how abysmal). Any help appreciated as I am not too familiar with complex numbers outside of the basics needed for transformation matrices.