Hmmm..what is the square root of minus one ???

Answer 1

It is correct that the square root of -1 is represented by the letter "i". However, just because it is called an "imaginary" number does not mean that it has no representation in the physical world.

Remember that an number is just an abstraction, and such a number might not make sense in a given context. For example the real, physical numbers 1/4 and 3/8 don't mean anything to someone counting stones.

In fact, "i" has a lot of real world, physical applications. Signal processing, control theory, electromagnetism, quantum mechanics, and cartography are all examples of where imaginary numbers have a real, physical representation just to name a few.

Imaginary numbers are also a way to explain the possible existence of worm holes, the theory of special relativity in four dimensions (the fourth being time), etc.

Aside from the real, physical representations of "imaginary" numbers, there are many mathematical analysis problems that would be grueling without the use of imaginary numbers. (Check out the study of Complex Analysis) In fact, there are dozens of trigonometric and other identities that electrical engineers use every day that would be nearly impossible to derive without imaginary numbers.

Finally, let me quote something from Jacques Hadamard:

"The shortest path between two truths in the real domain passes through the complex domain"

This means that "imaginary" numbers has been absolutely crucial to discovering truths in the the "real" number system over the years, and that is true.

The square root of -1 is a very real, physical number, just like 1/4, 3, and pi. For lots more information and application, check out "An Imaginary Tale" by Paul Nahin. It has a lot of difficult math, but it's a great read if you trudge through it.

Answer 2

1

Answer 3

U see if u put a square root into ur calculator it says error because there is no solution or possible answer for a negative square root. Because a neg. square root does not exist. Since they do not exist they are represented as "imaginary numbers" or i
You see i = the square root of -1
i^2 = -1 (since the square root of -1 times the square root of -1 is what is under the square root symbol) <-- you should already know that.....
i^3 = -i
i^4 = 1 (since -1 multiplied by -1) = 1<---- you should know this too.....
so then let's say the square root of -49 would not work in your calculator either then ur answer would be 7i since the square root of 49 is 7 and the negative would be represented with i....
another example would be the square root of -32 would not be 2i it would be 4i square root 2.......
Because look the square root of -32 is now going to become i square root of 32 and the 2 numbers that multiply to 32 since 32 is not a perfect square is 4 and 8...so since 4 is a perfect square the square root of 4 is 2...and 8 is not a perfect square unless ur looking for the cube root which then the cube root of 8 would be 2 but anywayz lol..I am just trying to help cuz this was diffulcult for me too....okay anywayz.....then u would find two numbers that when multiplied = 8 so 4 and 2. Again the 4 is a perfect square so that is 2 again....so now u have 2 times 2i with the square root of 2. So your answer would be 4i square root of 2.......I hope I helped u to completely understand the understanding of imaginary numbers....I am glad to have helped you....byez =)

Answer 4

i x 1

Answer 5

The square root of negative one is an imaginary number known as "the square root of negative one." In math, it's written as "i," which is short for "imaginary number." It's imaginary because any real number, positive or negative, will turn out a positive number when you square it. But it's useful in some calculations, so they use the letter i to represent it, because they have to use somehting.

Answer 6

There is no possible answer for the square root of minus one. nothing can multiply to itself and be negative. A positive and a positive is a positive, and a negative and a negative is a positive. A negative and a positive is a negative, but that isn't a square root problem, is it. So, to answer your question, the square root of one is...ALREADY SIMPLIFIED or i.

Answer 7

If you suppose there is such a number (call it "i" for short) so that i*i = -1, then (-1)*i also has the property that multiplying it by itself yields -1 also. By adding this number (and the product of it with every nonzero real number) to our usual numbers, you are able to solve every equation of the form ax^2 + bx + c = 0 (use the quadratic formula and algebraic manipulation to reduce the result in the form r + si.
What is amazing is that this simple addition yields practical results in problems like being able to map all the temperatures on a piece of metal by knowing the temperatures around its edges.
Since all numbers are abstractions, so-called "imaginary" numbers are just as "real" as the numbers we use to measure distance along a line!

Answer 8

The square root of -1 is an imaginary number and is termed as ' i ' for practical purposes.

Answer 9

The square root of -1 is an imaginary number defined as "i".

Answer 10

Like many people said before, it is an imaginary number represented by by the letter
" i ". And for your reference:
i^2= -1
i^3= -i
i^4= 1
and they repeat from there (i.e. i^5 is the same as i^ 1, i^6 is the same as i^2....)
the only real time this is used in real life (besides math) is in electrical engineering or other electircal stuff. (they use in terms of positive/negative of the AC(alternating current))