What is ($\sqrt{-1}$ or $i$) $\cdot$ $\infty$

Question

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.

Answer 1

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.

Answer 2

$x=\infty\cdot i$ is the most simplified it can get. It equals infinite imaginary things

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