# If ‘i’was invented to take the square roots of negatives, why can’t we invent a concept to divide by zero? [duplicate]

As explained in the title, if i is used to simplify expressions involving the square root of a negative number, is there another concept which allows us to simplify expressions involving zero on the denominator?

• – Hans Lundmark Oct 19 '19 at 9:21
• You can. But not without breaking things that we consider quite important. – Arthur Oct 19 '19 at 9:28

It was possible to extend the real numbers $$\mathbb{R}$$ to the complex numbers $$\mathbb{C}$$ and retain many of the familiar properties. This extension has proved to be very useful.
It is much harder to add infinity and retain many useful properties. It is done occasionally for specific purposes but generally not arithmetic; also the exact meaning will depend on the context. The familiar infinity symbol $$\infty$$ is commonly seen in limits but it is really just suggestive; the formal definitions don't usually involve infinity at all. In other cases, $$\infty$$ represents something more like naive infinity but it is not for arithmetic e.g. Extended real number line (Wikipeida)
But in certain cases we may write itm For example: equation of a line in $$3D$$, whose Direction ratios(DR) are $$(0,0,2)$$ and passing through the point $$(1,2,3)$$ can be written as $$\frac{x-1}{0} = \frac{y-2}{0} = \frac{z-3}{2} = t$$, where $$t \in R$$ is any parameter.
The parametric form the line (especially for x,y coordinates) can be obtained by "cross multiplying" their respective DR with the parameter equation to give $$(x,y,z)=(1,2,2t+3)$$.