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It is based on definition that you have to accept...which is:

i = the square root of -1

So, if you were to square i then you would get -1.

Hope that helped.

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Q: Why is an imaginary number squared equal to a a negative number?
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Does anything squared equal negative on and that number squared?

If I understand the question correctly, the answer is not in real numbers. But in the complex domain, there is the imaginary number i is such that i2 = -1. And so, for any positive x, [i*sqrt(x)]2 = i2*x = -1*x = -x, which is negative.


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What is the mathematical importance of imaginary numbers?

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Why do you say that pi is an imaginary number?

If I ask Answers™ "what is pi squared?" I find "It is approximately equal to 3.14 but in reality pi is an imaginary number that has no end." The answer also goes on to tell me that imaginary numbers cannot be multiplied by themselves. Now i must see what y'all have to say about imaginary numbers...


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