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What are imaginary numbers? - Mathematics Stack Exchange
You ask why imaginary numbers are useful. As with most extensions of number systems, historically such generalizations were invented because they help to simplify certain phenomena in existing number systems. For example, negative numbers and fractions permit one to state in a single general form the quadratic equation and its solution (older solutions bifurcated into many cases, avoiding ...
complex numbers - What is $\sqrt {i}$? - Mathematics Stack Exchange
This is one of the main reasons complex numbers are so important; they are the algebraic closure of the real numbers. You will never need "higher levels" of imaginary numbers or new mysterious square roots; numbers of the form a + bi a + b i are all you need to find any root of real or complex polynomials.
"Where" exactly are complex numbers used "in the real world"?
There are plenty of applications of complex numbers, but from what I have seen they are typically used to simplify solving a math equation, and the end result is still a real number. Or in some cases (lile quantum) a 2d vectors are represented with complex numbers, but could be represented with 2d vectors.
Solving Imaginary Numbers with TI89 Calculator - Physics Forums
Well I know it can solve for real numbers of X^n+x^ (n-1)+ etc etc = 0 But was wondering if it could also solve when there are imaginary numbers...
Why don't we define "imaginary" numbers for every "impossibility"?
Particularly for the imaginary numbers you mentioned, the square root of $-1$ was contemplated because it simplified manipulations on polynomials when looking for their roots.
Are there imaginary numbers other than i? • Physics Forums
Participants examine theoretical constructs, alternative number systems, and the philosophical implications of defining numbers. One participant questions whether there are "imaginary" numbers other than i, suggesting that if utility is the standard for creating numbers, other complex families could exist.
Rules of imaginary numbers - Mathematics Stack Exchange
Rules of imaginary numbers Ask Question Asked 10 years, 11 months ago Modified 2 months ago
Historical Motivation for the Creation of Complex/Imaginary Numbers?
Does anyone know from a historical perspective what kinds of problems/situations resulted in the need and creation of complex/imaginary numbers? Recently, my friend was asking about why we need complex numbers and what are there applications.
imaginary numbers - how can I understand them - especially as they ...
13 In another question here, about roots of equations being imaginary, the accepted answer said something interesting about "imaginary" (as a technical word in math) not meaning "not real". I understand that imaginary numbers are "manipulable and usable to do all kinds of things". And thus, "they exist" at least, in the realm of mathematics.
Why are imaginary numbers called "imaginary"? If they really exist
The discussion centers around the terminology of "imaginary numbers," exploring the reasons behind this nomenclature despite their real applications in mathematics and physics. Participants delve into historical context, definitions, and the implications of using the term "imaginary" in various mathematical frameworks. Some participants assert that imaginary numbers are called "imaginary" due ...
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