Imagining the imaginary

Relevant wiki: Euler's Formula

$\begin{aligned} \ln(i^i) & = i \ln \color{#3D99F6} i & \small \color{#3D99F6} \text{By Euler's formula: } e^{\frac \pi 2 i} = \cos \frac \pi 2 + i \sin \frac \pi 2 \\ &= i \ln \left ( {\color{#3D99F6}e^{\frac \pi 2 i}} \right) \\ &= i \left (\frac \pi 2 i \right) \\ &= - \frac \pi 2 \end{aligned}$

$\implies k = \boxed {-0.5}$

why level 4 , it is very very easy ! no offence , they just giving rating to anything ! at most level 2 !

$\begin{aligned} \large{i^i} & = \large{{\left(e^{i × \frac{\pi}{2}}\right)}^{i}}\\ \\ & = \large{e^{-\frac{\pi}{2}}}\\ \\ \implies \large{\ln(i^i)} = \large{-\dfrac{\pi}{2}}\\ \\ \implies \large{k} = \large{\color{#69047E}{\boxed{-0.5}}} \end{aligned}$