TITLE: Is $i$ equal to $\sqrt{-1}$?
QUESTION [6 upvotes]: Some of my math teachers said that $i=\sqrt{-1}$ is the wrong definition for $i$ and that the correct definition is $i^2=-1$. If the second definition if true, then does it mean $\sqrt{-1}= ±i$? Which of the two definitions is true?

REPLY [2 votes]: $\sqrt{-1}$ is denoted as $i$ and $i$ is a solution of the algebraic equation $x^2+1=0$. That is why $i^2=-1$.
One could define $i=-\sqrt{-1}$ and using this notation he could built the Complex analysis. That is up to him.