2006-08-31 07:35:24 · 23 answers · asked by david12strings 1 in Science & Mathematics ➔ Mathematics
The square root of negative one DOES exists. By definition, it is "i".
Claims of its nonexistence are confused with it not being a real number. It's called an imaginary number, but not because it doesn't exist. It's called an imaginary number because it is not real (and the word "real" in math lingo simply means a number on the number line that everyone is familiar with. It doesn't imply that other numbers do not exist.)
To give you an advantage to what it seems like you about to do in math, keep in mind the following two things about the number i, and most complex arithemetic will be easy (complex meaning "of the form a + bi", not complex meaning "hard")
1) If you ever square root -1, replace that with an i.
Example: sqrt(-9) = sqrt(9) * sqrt(-1) = 3i
2) If you ever square an i, replace it with -1.
Example: (3i)(6i) = 18i^2 = 18(-1) = -18.
I know, I know, "I thought when you square something, it comes out positive?" Yeah, that's a rule... for REAL numbers. "i" is not real. It is imaginary. It plays by its own rules.
2006-08-31 07:46:19 · answer #1 · answered by Anonymous · 4⤊ 0⤋
It does not exist. But guess what? A whole branch of mathematics called complex analysis is built around this idea.
'i' is definitely not a real number as michaelduggan writes. His understanding has limits. In fact to say i*i = -1 is not strictly speaking correct either. However, combined with the properties of trigonometric functions, one can arrive at DeMoivres' and Euler's well-known formulas. By the original definition of square, the square of a number is always positive.
2006-08-31 09:49:40 · answer #2 · answered by Anonymous · 0⤊ 1⤋
The square root of minus one practically does not exist.
However, a notation given to it is "i" (iota).
That is the root of minus 1 is i
Or else for example root of -4 is 2i (root of 4 * root of -1)
It is known as a complex /imaginary number.
2006-08-31 07:40:33 · answer #3 · answered by Anand 2 · 5⤊ 0⤋
simple the answer is i
i squared = minus 1
2006-08-31 07:44:16 · answer #4 · answered by Anonymous · 1⤊ 0⤋
It's impossible, so that is why they invented the imaginary number i. so whenever you end up with root of neg. 1 you can substitute that with an i.
Good luck!
2006-08-31 08:45:21 · answer #5 · answered by Marla 3 · 0⤊ 0⤋
No, there cannot be square root of a negative number, however, there can be a negative square root of a positive number.
2006-08-31 07:44:54 · answer #6 · answered by Sniper 4 · 0⤊ 2⤋
since negative numbers cannot have square roots, the number is deamed imaginary. Therefore we designate a smaller case " i " as the answer.
2006-08-31 07:42:00 · answer #7 · answered by sewshawn 3 · 2⤊ 1⤋
-1 has no real square root. It has two imaginary square roots, "i" and "-i".
2006-09-04 04:50:18 · answer #8 · answered by bh8153 7 · 0⤊ 0⤋
square root of minus one or any other negative number is not possible.
2006-08-31 07:38:58 · answer #9 · answered by knowbuddycares 3 · 0⤊ 3⤋
1 ?
2006-08-31 07:41:17 · answer #10 · answered by ? 4 · 0⤊ 2⤋