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Let:

$x=\infty\cdot i$

$y = \frac{\infty}{i}$

Find $\ x\ $and$\ y.\ $

Does this even make sense? Would $x$ just be $\sqrt{-\infty}$?

I'm confused as to what's going on here.

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closed as unclear what you're asking by Xander Henderson, let's have a breakdown, Hans Lundmark, Saad, Namaste Mar 1 '18 at 0:42

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Note that $\infty$ is not a number then these expressions

  • $x=\infty\cdot i$
  • $y=\frac{\infty}{i}$
  • $\sqrt{\pm\infty}$

are, in the usual context, meaningless.

In some cases, notably when we deal with limits, we can use expressions like:

  • $\infty\cdot\infty$
  • $\frac{\infty}{\infty}$
  • $1^{\infty}$
  • $i\cdot\infty$
  • etc.

but they are to be intended as symbolic expressions with the aim to express, in a short term, whether an expression is or not in an indeterminate form.

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  • 1
    $\begingroup$ I took the liberty of adding $i\cdot\infty$ to the list. In some contexts, for example when dealing with the upper half-plane, it serves a role as a "limit point at the end of the imaginary axis". Comes to the fore when dealing with modular forms and such. Admittedly it is unlikely to be relevant to the asker. $\endgroup$ – Jyrki Lahtonen Mar 1 '18 at 13:46
  • $\begingroup$ @JyrkiLahtonen Thanks so much for your kind contribution! And I have to admit that it is unlikely also to me but it is very stimulating to know! Thanks again. $\endgroup$ – gimusi Mar 1 '18 at 13:49
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$x=\infty\cdot i$ is the most simplified it can get. It equals infinite imaginary things

$y= \frac{\infty}{i} = y = \infty \cdot -i$

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