Does anyone else see the relavence in "imaginary Numbers?"?

Question

I got in an argument today with my College Algebra and Trig (cat) professor about the fact that "imaginary numbers" are pure bullshit. You simply cannot get an answer for a negative square root. so, does anyone have any logic reason why the exsist other than to appease the people who think there HAS to be an answer for everything?

ok, so many of you are saying it's important in engineering and electics..but how so? i dont' see how FAKE NUMBERS can help you get a REALISTIC answer...?

none of you are answering my question though...HOW (and i put emphasis on how) is it relavant? how can a FAKE number be used to calculate electronical stuff? i mean...if it's IMAGINARY how can it be applied to real life situations?

Answer 1

By using Euler's' identity. It allows one to solve differential equations using simple algebra. One can convert a differential equation to it's imaginary equivalent, solve it using algebra (which is easier than any other method for solving differential equations), and then convert back to real numbers.

Normally one uses calculus to solve differential equations. Much harder.

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Applications of imaginary numbers

Despite their name, imaginary numbers are as "real" as real numbers.[2] (See the definition of complex numbers on how they can be constructed using set theory.) One way to understand this is by realizing that numbers themselves are abstractions, and the abstractions can be valid even when they are not recognized in a given context. For example, fractions such as ⅔ and ⅛ are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Similarly, negative numbers such as − 3 and − 5 are meaningless when keeping score in a US football game, but essential when keeping track of monetary debits and credits[1] (or yards gained on a play in the same football game).

Imaginary numbers follow the same pattern. For most human tasks, real numbers (or even rational numbers) offer an adequate description of data, and imaginary numbers have no meaning; however, in many areas of science and mathematics, imaginary numbers (and complex numbers in general) are essential for describing reality. Imaginary numbers have essential concrete applications in a variety of sciences and related areas such as signal processing, control theory, electromagnetism, quantum mechanics, and cartography.

For example, in electrical engineering, when analyzing AC circuitry, the values for the electrical voltage (and current) are expressed as imaginary or complex numbers known as phasors. These are real voltages that can cause damage/harm to either humans or equipment even if their values contain no "real part". The study of AC (alternating current) entails introduction to electricity governed by trigonometric (i.e. oscillating) functions. From calculus, one knows that differentiating or integrating either "+/- sin(t)" or "+/- cos(t)" four times (with respect to "t," of course) results in the original function "+/- sin(t)" or "+/- cos(t)." From complex algebra, one knows that multiplying the imaginary unit quantity "i" by itself four times will result in the number 1 (identity). Thus, calculus can be represented by the algebraic properties of the imaginary unit quantity (this was exploited by Charles Proteus Steinmetz).

Specifically, Euler's formula is used extensively to express signals (e.g., electromagnetic) that vary periodically over time as a combination of sine and cosine functions. Euler's formula accomplishes this more conveniently via an expression of exponential functions with imaginary exponents. Euler's formula states that, for any real number x,


Some programming languages also have built-in support for imaginary numbers. For example, in the Python interpreter, one may use them by appending a lowercase or uppercase J to the number...

Answer 2

Ask yourself this question then... why the hell do we have negative numbers.. I mean.. you can't have NEGATIVE of something can YOU?!? That's crazy!

I have negative 2 cats! Nuts man! Nuts I tell ya!

Point is.. imaginary numbers are as "real" as "real" numbers. For example, fractions such as ⅔ and ⅛ are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Similarly, negative numbers such as − 3 and − 5 are meaningless when keeping score in a US football game, but essential when keeping track of monetary debits and credits[1] (or yards gained on a play in the same football game).

Imaginary numbers follow the same pattern. For most human tasks, real numbers (or even rational numbers) offer an adequate description of data, and imaginary numbers have no meaning; however, in many areas of science and mathematics, imaginary numbers (and complex numbers in general) are essential for describing reality.

Answer 3

It allows you to proceed with further mathetical work and sometimes obtain a real number. Once you reach the square root of a negative number, in theory, you cannot proceed any further. But if you replace the square root of -1 with 'j', you can proceed. Sometimes the final answer may hold a 'j^2' which is equal to + 1.

Answer 4

Imaginary numbers are used in engineering e.g. in complex calculation such as the aerodynamics of a wing on a plane.

Answer 5

False, there is relevance for imaginary numbers later on when you take abstract algebra in College and work for electrical engineering. And plus i is cool.

Answer 6

I'm down with what you're saying. If you need back-up in class, give me a call. I'll wear a ski mask and a shirt with the words "UN- Imaginary FOR LIFE" on it.

Answer 7

You're just jealous because THE VOICES AREN'T TALKING TO YOU

They also weren't talking to some of those greek mathematicians who couldn't wrap their head around "irrational" numbers. Heresy!

Answer 8

The trouble with imaginary numbers is that they're not imaginary.

Answer 9

Everything in math don't have to be real.
Now you are an imajinary student for me, aren't you?

Try to learn what you can do with complex numbers.

Answer 10

if there is no imaginary numbers then there won't be any electricity, circuits, computers, TV, playstations...oh god...horrible...noooooooooooooooooo...
SO there you have it..we must have imaginary number :)