Why does imaginary numbers have their logic in numbers? And how can they be applied in life?

Answer 1

Before there were negative numbers, mathematicians
just said that subtracting a larger number from a smaller
number was impossible or that the answer was not real.
blah-blah-blah.
Before there were fractions and decimals mathematicians
said that dividing a number by something other than a factor
of it could only give you an approximation or a number with a
remainder, blah-blah-blah..
Before there were imaginary numbers mathematicians said
that you could not take the square root of a negative number,
blah-blah-blah.
But in each case, new innovative mathematicians came thru
and extended our manipulation of math.
Imaginary numbers have a lot of application in electronics
for one. But I love them 'cuz I can compute things like the
3 square roots of -1 and most people can't.

Answer 2

sometimes they make doing math problems easier. For instance, those trig identities you spent so much time memorize for test.... Well, i don't know them, but i know how to get them really easily using imaginary numbers.

Another reason we need them is some problems are not solvable in the Reals (the numbers you are use to). Sometimes you need to use imaginary numbers in order to be given more space to solve a problem. This is true of quantum mechanics where there is no solution to many problems without using imaginary numbers. Does this mean that we are able to observe the solution when we are finally done? Well no, we need to multiply by complex conjugates in order to bring it back to reality, but the problem itself wouldn't be solvable without the imaginary numbers.

You might be confused because the first place they come up is in the quadratic. The teacher usually says something like "these are the imaginary answers to the problem." Meaning the graph doesn't actually cross the x-axis (the thing we were solving for), but we can fudge something and get answers anyway. I am not convinced, and you are probably resistent also. The problem is that they also come up in the cubic equation... the equation used to solve polynomials that look like this:

Ax^3 + Bx^2 + Cx+ D = 0

What is the big deal? Well look at the graph of a cubic: http://content.answers.com/main/content/wp/en/thumb/7/76/200px-Polynomialdeg3.png

IT MUST CROSS THE X-AXIS. So in order to use the equation for the cubic we must either accept imaginary numbers or throw out an equation we know works! Now, what would you do?

Answer 3

The fact of the matter is, underneath it all, ALL numbers are imaginary anyway. Have you seen the number 2? I haven't seen the number 2. I've seen the SYMBOL 2, but not the number. There's nothing to see, because it's imaginary, and one can only use concepts ABOUT the number 2, but not really know what it is.

The same thing goes for i = sqrt(-1).

If you want a certain answer on how they're applied in life, the television would never have been invented if it weren't for i, because i is used for rotating vectors.

Answer 4

different than the electronics already stated, they are able to be utilized in section equations in circuits. additionally, you may symbolize vectors with them and picture each and each vector having a real and a non-genuine factor. Then, you may upload, subtract, multiply, and divide the vectors and have it advise something. As for the non-engineering purposes, there are coding theories, complicated diagnosis, present day algebra, style concept, and different much less utilized factors of arithmetic that use them drastically. they are able to be the solutions to 3 trig issues which would be very tricky to do without them. DeMoivre's theorem comprises techniques as a thank you to looking the non-genuine roots of a million. those can then be used to transform some around/trig representations into complicated style representations.