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Negative 1
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True, but it's not really a teaser - that's essentially the definition of i.
It's like asking "how many sides does a triangle have"? Either you know it or you don't.
It's like asking "how many sides does a triangle have"? Either you know it or you don't.
Actually the square root of -1 is -1. -1 times-1 = -1 and that is what square root is.
sorry smileysteve but -1 X -1 = 1 not -1... when u multiply 2 negavitve numbers, ur left wiht a posiitve
you cannot take a square root of a negative number and get an actual number without having i by it. Sqrt of -9 = 3i
The 1 coefficient was not required in the answer. And, I agree, it's not really math, but simply knowledge.
Same comment: this is just knowledge, not a teaer. Either you know it or you don't.
Sorry the answer is still wrong. The set of complex numbers, unlike real numbers, are not a signed number set - that is you do not have just a positive set and a negative set on the number line. Yes you can use the + and minus signs but (1 + 3i) and (1 - 3i) cannot be said to be either positive or negative. When we ask for the square root of a number in the real number system we present only a positive number. So 5 x 5 = 25 and (-5) x (-5) = 25 also but the square root of 25 is just 5 (not -5). Try it on a calculator if you like. Square root is a single valued function!
Now when it comes to complex numbers, you cannot single out positive complex numbers from negative complex numbers so traditionally we should ask for the square roots (plural - there will always be two of them). The answer to the question what are the square roots of -1 is either i or -i.
Now when it comes to complex numbers, you cannot single out positive complex numbers from negative complex numbers so traditionally we should ask for the square roots (plural - there will always be two of them). The answer to the question what are the square roots of -1 is either i or -i.
Sorry - just to clear up the definition of i. The definition of i is that i^2 = -1. It should not involve a square root sign.
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