According to the great well-known Euler's formula:
$$e^{i\theta} = \cos\theta + i\sin\theta$$Let $\theta = \pi/2$, then:
$$\begin{align*} e^{i \pi / 2} &amp;= cos(\pi/2) + i sin(\pi/2)\\ &amp;= 0 + i \times 1 \\ &amp;= i \end{align*}$$Now, doing a substitution $i$ with $e^{i\pi/2}$:
$$i^i = (e^{i \pi / 2})^i = (e^{\pi / 2})^{i^2} = e^{- \pi / 2} =0.207879…$$How beautiful!

According to the great well-known Euler's formula:

$$e^{i\theta} = \cos\theta + i\sin\theta$$

Let \$\theta = \pi/2\$, then:

$$\begin{align*} e^{i \pi / 2} &= cos(\pi/2) + i sin(\pi/2)\\ &= 0 + i \times 1 \\ &= i \end{align*}$$

Now, doing a substitution \$i\$ with \$e^{i\pi/2}\$:

$$i^i = (e^{i \pi / 2})^i = (e^{\pi / 2})^{i^2} = e^{- \pi / 2} =0.207879…$$

How beautiful!

What is i^i?

...interesting things by short notes and demos. Most of notes are in Vietnamese since too few of resources of the language and machine translation EN-VN are not good enough :)
