Giving this power equation: $$S=\lim_{n\to\infty} {^n}x=-i$$ where the symbol $^nx$ means the tetration operator, we can write in a form not formally correct: $${\ ^{n}x = \ \atop {\ }} {{\underbrace{x^{x^{\cdot^{\cdot^{x}}}}}} \atop \infty}$$ which must be equal to $-i$. So we can write $x^{-i}=-i$ and then $x=\exp \left(\dfrac{\pi}{2}+2k\pi\right)$
For $k=0$ we have: $x=\exp(\pi/2)\simeq 4.81$. So: this means: $$\lim_{n\to\infty} {^n4.81}=-i$$ But also, for $k=2$, we can write $\lim_{n\to\infty}{^n}2575.9=-i$
This means: putting: $a=\exp\left(\dfrac{\pi}{2}+2k\pi\right)$ $${\ \atop {\ }} {{\underbrace{a^{a^{\cdot^{\cdot^{a}}}}}} \atop \infty}=-i$$
If we change $-i$ with $i$, we found the same result. Is this a correct result? Thanks