43 questions linked to/from Do complex numbers really exist?
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### difficulty of accepting $i^2 = -1$ for first timers [duplicate]

While teaching complex numbers for those who are encounter for the first time (usually 10th grader and 11th grader), I get the question like "Can even squared number give negative results? How ...
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### Why is $i^2$ equal to $-1$? [duplicate]

In this KhanAcademy link at 2:25, Sal (the narrator) says that $i^2$ is negative 1 and he didn't explain why. Why is this so? What is the intuition behind it?
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### Imaginary Numbers

I imagine there have been many questions about imaginary numbers, so if I am asking a question already answered my apologies. I understand that it is perfectly correct to create new number systems ...
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### Refining my knowledge of the imaginary number

So I am about halfway through complex analysis (using Churchill amd Brown's book) right now. I began thinking some more about the nature and behavior of $i$ and ran into some confusion. I have seen ...
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### Why does the imaginary number $i$ satisfy $i\times 0=0$?

Why does the imaginary number $i$ satisfy $i\times 0=0$? I mean, we don't really know what $i$ is. How could we be sure about that? I think there's a reason behind why mathematicians decided that.