User blog:Cheetahrock63/Complex googolism things

so here are a bunch of unimportant complex googolisms created by lazily slapping affixes onto $$i$$. they're listed by absolute value (distance from 0) from least to greatest.

there are expressions that are multi-valued, for example, $$i^i$$ is equal to $$e^{\frac{-\pi}{2}}$$, $$e^{\frac{-5\pi}{2}}$$, $$e^{\frac{-9\pi}{2}}$$, etc. but for simplicity's sake, we'll just forget about them and use only the principal values

nothing here contributes anything new to the googological field, but i figured it's not illegal for me to dump it here (is it?)

Fzi $$= i^i = e^{\frac{-\pi}{2}} \approx 0.20788$$

Iduplex $$= 10^{10^i} = e^{10^i(\ln{10})} \approx -0.03044 + 0.21251i$$

Gari $$= i^2 = e^{\pi i} = -1$$

Iplex $$= 10^i = e^{(\ln{10})\cdot i} \approx -0.6682 + 0.74398i$$

Fugai $$= i^{i^{i-1}} = e^{\frac{i^i\pi}{2}} \approx 1.38616$$

Ity $$= 10i = 10\cdot e^{\frac {\pi i}{2}}$$

Iteen $$= 10 + i = \sqrt{101}\cdot e^{(\arctan{\frac{1}{10}})\cdot i}$$

then there's also $${}^xi$$ as $$x$$ approaches infinity, which has the limit of $$0.4382 + 0.3606i$$ (funny how infinite tetration of i actually approaches a value whereas other functions like exponentiation or multiplication don't)