Is $i$ a positive number? This question came to mind when I saw a way of finding the value of $i^i$ which included transforming it to $e^{i\ln(i)}$ and taking $\ln(i)$ as $i\frac{\pi}{2}$
I understand how we can get $\ln(i)$=$i\frac{\pi}{2}$ geometrically but this got me thinking if $i$ is a positive number as the first thing I learned about $\ln$ since high school days is that it can't take negative numbers. 

The sign can be defined as:
$$
sgn(x)=\begin{cases}
\frac{x}{|x|},  & \text{if $x \neq 0$} \\
0, & \text{if $x = 0$}
\end{cases}
$$
If you extend this to complex numbers, the sign can be any complex unit or zero. In that way $sgn(i)=i\neq0$ so it's not positive.
We usually don't define positive and negative numbers in the means of complex numbers. Some literature define it in the way I have shown above and then "$z$ is positive" implies that $\Im(z)=0$.
