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I played with imaginary numbers while in college.

I've made some mind-stretching "discoveries" over the years.

I'll post some of them here, a few at a time.

If any of you have found such "facts", I've love to see them.

Consider a line with slope $i.$

. . It would have the form: $y \:=\:ix + b$

Since $i = \text{-}\frac{1}{i}$ ($i$ is its own negative reciprocal),

. . the line $y \:=\: ix + b$ is perpendicular to itself.

Consider the circle $x^2+y^2 \:=\:\text{-}1$.

. . It has center $(0,0)$ and radius $i$.

Its area is: $\pi(i^2) \:=\:\text{-}\pi$, a real number.

Surprisingly, $i^i$ is a real number: .$i^i \:=\:e^{\text{-}\frac{\pi}{2}}$