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My PreCalculus teacher recently reviewed the properties of limits with us before our test and stated that any real number divided by infinity equals zero. This got me thinking and I asked them whether a complex number (i.e. $3+2i$ or $-4i$) divided by infinity would equal zero.

This completely stumped them and I was unable to get an answer. After doing some theoretical calculation, knowing that $i=\sqrt{-1}$, I calculated that a complex number such as $\frac{5i}{\infty}=0$ since $$\frac{5}{\infty}\cdot \frac{\sqrt{-1}}{\infty} = 0\cdot 0 = 0,$$ using properties utilized with real numbers that would state that $\frac{5x}{\infty} = 0$ since $$\frac{5}{\infty}\cdot \frac{x}{\infty} = 0\cdot 0 = 0.$$ Is this theoretical calculation correct or is there more to the concept than this?