How do IMAGINERY Number exist?

Question

If they are MAGINERY, like IMAGINERY friends,
then how can they exist?

SQR 1 = i?

Answer 1

Physics:
http://answers.yahoo.com/question/index;_ylt=ArBv6i0ByRlxiMrMRAEY3Fz4xQt.?qid=20070619064431AA4Xsic

Mathematics:
http://answers.yahoo.com/question/index;_ylt=Avuw_Kyx9neqbEUfJK7w8Xj4xQt.?qid=20070619064313AAIJOB2

Engineering:
Don't be ridiculous. Imaginary things are of no value in engineering, except they can be used as a shortcut to getting to an answer or quantity of actual value.

But seriously:
Imaginary numbers are the solutions to equations such as x^2+9 = 0. The parabola described never crosses the x-axis; but still this equation has an imaginary solution.

Presented in this way, it is hard to imagine that such a thing could ever be useful. The real value of imaginary numbers comes out of power series expansion of functions.

Any function can be represented by a power series (Taylor series or Maclaurin series) a0 + a1*x + a2 x^2 + a3 x^3 +...

Many properties come from this; one is that the math of trigonometric functions, such as sine and cosine can be greatly simplified by using imaginary numbers.

Damped harmonic motion, which oscillates as it fades, for instance, can be described mathematically, much more simply with complex numbers.

Take the function y=e^(a*t), where a is a complex number. The real part of a will cause the function to exponentially decrease over time, as the energy is released from the system. The imaginary part will cause the function to oscillate, as kinetic energy phases into potential energy, or vice versa.

Though both the kinetic and potential energies are real things, it is convenient to have this mathematical quantity whose literal value is the square root of negative one available to work with, even though I would be hard pressed to think of any real quantity which could be called imaginary.

Answer 2

in a simple answer, the imaginery number is only a term. Usually used in calc classes when looking at graphing. As you continue, the term complex number will come into play.

It is just a way of introducing a number system in which you will build upon as you continue to learn.

You can think of a x and y graph where the non-imaginery number is the x and the imaginery number is in the y direction.

so if it makes you feel better, use the term complex.

Answer 3

It's just a name. Imaginary numbers are a covenient way to do math on a system that has numbers with elements ar right angles to each other.

Answer 4

The same way dragons, unicorns, and moon hoax theories do - in our minds only. But that doesn't mean we can't use them to solve problems in electronics, for which they can be handy.

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Answer 5

These are philosophical truths just like '0' or infinity . You can not count them physically.