"The true metaphysics of the square root negative 1 remains elusive." - C.F. Gauss

IBDaMann said:
That is the definition. If you are operating under the assumption that I was the one who authored the definition, you are mistaken.


Correct. You can't take the square root of negative numbers, but I see that you are too stupid to learn even something so simple and straightforward.


Yes. That, I do. I also call you too-stupid-to-learn. I wonder why you feel the need to gibber on math.


If you would care to research the mathematical proof that shows you to be utterly mistaken, you'd see that you cannot take the square root of negative numbers.

I see that you still haven't researched that proof. I see that you believe you get to make up your own math.
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A brilliant analysis from the Great Thinker from someplace in outer space.
 
EdwinA said:
Well, we know Ida isn't an engineer or a physicist.

The Peanut Gallery might be interested in what practical purpose there is for complex numbers.

https://en.wikipedia.org/wiki/Euler's_formula

en.wikipedia.org

File:Rising circular.gif - Wikipedia

en.wikipedia.org en.wikipedia.org
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He's more of a frantic Googler than an engineer.

I was impressed with how many electrical engineers and physics majors chimed in helpfully on this thread.

My only direct connection to complex numbers was in high school and college math, plus whatever I've read about it in popular science articles.
 
Cypress said:
He's more of a frantic Googler than an engineer.
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Preemptive projection on your part.

Cypress said:
I was impressed with how many electrical engineers and physics majors chimed in helpfully on this thread.
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Nobody chimed in with the correct answer. All but one or two were completely mistaken.

Cypress said:
My only direct connection to complex numbers was in high school and college math,
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Who do you expect is going to believe that you finished high school?

Cypress said:
plus whatever I've read about it in popular science articles.
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You didn't read any science articles. You read gibberish from self-agrandizing losers who know they can count on fooling scientifically illiterate and mathematically incompetent morons such as you and others like you.
 
AProudLefty said:
I am asking you nicely. Please provide the proof.
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Sure.

In mathematics, it is common knowledge that it is not permissible to take the square root of negative numbers. All children who don’t regularly play hooky are taught this because it is crucial to avoiding common pitfalls in algebra. Many adults, however, forget this and end up operating under the bogus misconception that complex numbers are somehow all about taking the square roots of negative numbers and that the imaginary number i is somehow defined as being the square root of -1.

Most adults who operate under this misconception are too embarrassed at being reminded of what they had long since forgotten to correct their misunderstanding. Instead, they tend to double down on the idea of committing math errors as somehow being legitimate. Otherwise, the mathematical proof is straightforward for those who simply want to understand why taking the square root of negative numbers is not permissible. The lesson to be learned here is that because there is no such thing as the square root of any negative number, any calculation involving such can have any resulting value, and if every value is the correct result then no value is the correct result. Let’s look at the proof.

This particular proof is a reductio ad absurdum, or proof by contradiction. We start by assuming that everything is just fine with taking the square root of negative numbers, and that i = √-1 then we see what happens.

Let’s do some math:

-1 = i *i = √-1 * √-1 = √(-1*-1) = √1 = 1

*… so, we see that if we permit i = √-1 then -1 = 1,
* adding one to each side yields 0 = 2, and finally, dividing by 2 on each side gives us 0 = 1.
* now we know that 0 = 1 = 2.
* If we keep going, we show that 0 = 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9
* This means that 457.2403 = 017.6200 = 000.0013 = 977.5939
* All numbers equal every other number
* An atomic mass of 15.999 u = an atomic mass of 10.81 u = an atomic mass of 207.2 u
* ergo Oxygen is Boron is Lead. In fact, every element is every other element.
* Every mass is every other mass. Your mass equals the mass of the nearest black hole
* The space shuttle is a handful of gravel
* 14.6 miles per hour = mach 3. All momentums are equal. All velocities are equal.
* All attributes are every other attribute.
* Global Warming is Global Cooling is no change whatsoever.
* All distances are equivalent
* All time spans are equivalent

Also, since we know that it is FALSE that 0 = 1, and we have just shown that it is TRUE that 0 = 1, we have shown that TRUE = FALSE. Thus every statement is both TRUE and FALSE.

Either we have a major breakthrough … or we must conclude that our assumption about defining i = √-1 is what is FALSE. In fact, the above proof holds for any negative number for which one tries to take the square root.

What this proof tells you is that an attempt to perform mathematical calculations using square roots of negative numbers can result in any answer. In fact, any desired outcome can be calculated without making any other math errors. In any system that permits the taking of square roots of negative numbers, if the desired answer is 55.914 then that answer can be arranged. That’s not how we want math to work.
 
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+1

Imaginary Numbers are Real – Galileo's Pendulum

Yes, the square root of -1 does exist within the realm of complex numbers. It is represented by the imaginary unit, denoted as "i". Therefore, the square root of -1 is equal to i, where i² = -1.

Elaboration:
  • Real Numbers:
    In the standard real number system, there's no real number that can be squared to produce a negative number. This is because squaring any real number (positive or negative) always results in a positive number or zero.

  • Imaginary Numbers:
    To address the square root of negative numbers, mathematicians extended the number system to include imaginary numbers. The imaginary unit "i" is defined as the square root of -1.

  • Complex Numbers:
    Complex numbers are a broader system that includes real and imaginary numbers, expressed in the form a + bi, where 'a' is the real part and 'b' is the imaginary part.

  • Mathematical Significance:
    Complex numbers, including the imaginary unit, are crucial in various fields like physics, electrical engineering, and signal processing. They allow us to solve problems that are not possible within the real number system alone.
 
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