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Even though there is no real answer to the equation √-1, we give it the symbol i.

What is the reason that there is a symbol for √-1, but no symbol for dividing by zero?

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marked as duplicate by Chris Culter, user63181, MJD, mathematics2x2life, Ryan Budney Jan 19 '14 at 7:52

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There can be many possible answers to your question.

  1. $\sqrt{-1}$ has a root symbol and writing it again and again will be quite boring as well as confusing because when writing on paper over a long period then it may be possible that a variable falls in the that root sign (by mistake).

  2. We have branch of complex numbers and we use Re-Im graph in which imaginary axis is plotted with multiple of $\sqrt{-1}$ so we use i to denote $\sqrt{-1}$.

  3. For ${\frac{a}{0}}=b,$ a not equal to 0.

$\implies b.0=a $

Now for which b the equation is valid, and you will find that there exist no value of b that satisfies the above equation.

So giving a symbol to this expression is useless.

What is the value of $b^{2}$? but $i^{2}=-1$

  1. For what $\infty$ is defined? It is for b

Now you tell what will be $b^{2}$ it will not be $\infty$.

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