# Should you write $i = \sqrt{-1}$ or $i := \sqrt{-1}$?

Is one of the following more correct than the other, or does it simply not matter?

$$i = \sqrt{-1} \quad$$ or $$\quad i := \sqrt{-1}$$?

Here I am using $$:=$$ to mean "defined to be equal to."

• I wouldn’t write either. – Randall Nov 28 '18 at 12:28
• @Randall okay, what could you write instead? – Gurjinder Nov 28 '18 at 12:32
• @Randall Do you mind expanding on this comment? Otherwise is not very useful for the OP – caverac Nov 28 '18 at 12:32
• $i^2=-1$........ – Randall Nov 28 '18 at 12:32
• @caverac You are correct. Fair point. – Randall Nov 28 '18 at 12:33

None of them are correct as the square root is not a single-valued function. The best expression (i.e. simplest) defining $$i$$ would be $$i^2=-1$$.
• Okay fair enough. Why not $i^2 := -1$? – Gurjinder Nov 28 '18 at 12:37
• Okay, I think the OP had an error. Let's think about $i$ as $\pm\sqrt{-1}$. $i=\pm\sqrt{-1}$ or $i:=\pm\sqrt{-1}$? – manooooh Nov 28 '18 at 12:39
• You can write that. $:=$ is usually used in definitions. Since $i$ is widely used, we don't need to "define" it everytime. Also, that notation is hardly ever used. But if you want, no one is stopping you (possibly once in a discussion/problem). – SinTan1729 Nov 28 '18 at 12:39