Rotation multiplying by $i$ in complex numbers

Question

In comparison to $\arg(z)$, what would $\arg(zi)$ look like?

My answer: Rotation by $-\pi/2$, which adds $\pi/2$ to the argument.

Friend: Rotation by $\pi/2$, which minuses $\pi/2$ to the argument.

:( This might be stupid so sorry in advance haha

Answer 1

Since $i=\exp\frac{\pi i}{2}$, $\operatorname{arg}(zi)\equiv\operatorname{arg}(z)+\frac{\pi}{2}(\bmod 2\pi)$. A restriction of arguments to an interval of length $2\pi$ obtains $\operatorname{arg}(zi)-\operatorname{arg}(z)\in\{-\frac{3\pi}{2},\,\frac{\pi}{2}\}$.