After solving a bunch of stuff I got to $\ arg(1/-i)$. What does this mean geometrically, and moreover, will the conjugate of $i$ be $-i$ or just $i$ itself?
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$\begingroup$Geometrically the conjugation of a complex number corresponds to taking its reflection with respect to the $x$-axis. In the case of $i$, you can think of it as the point $(0,1)$ in the plane. Therefore its reflection with respect to the $x$-axis is the point $(0,-1)$ which is $-i$.
The result you obtained is consistent with this since $1/-i=i/i^2=i$.
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