Sep 20, 2012 · 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 …

May 2, 2017 · $\\mathbb Q$ is used to represent rational numbers. $\\mathbb R$ is used to represent real numbers. Is there an accepted symbol for imaginary numbers?

Jul 7, 2023 · First of all, complex numbers are two-dimensional, having independent x (real) and y (imaginary) components. This makes it possible to define a “rotation”, which you can't really do …

Why do we call imaginary numbers "imaginary numbers"? As far as I can tell, there's nothing really imaginary about them. They exist. They're used all the time. What makes them so …

Apr 6, 2017 · Clearly we can (re)define a real number as a complex number with an imaginary component that is zero (meaning that 0 0 is a real number), but if one were to define an …

Imaginary exponents are just the same. i, 2i, 3i are just like 1, 2 ,3: identity, square, and cube. They just need to run into another imaginary exponent to manifest their value, or you are …

Dec 26, 2007 · if we define 'imaginary numbers' as 'complex numbers having a real part as 'zero' and a non-zero imaginary part'.. 0 doesn't fit in this description. But by, convention and for …

Feb 21, 2016 · This sort of question is answered by looking at the precise definitions. How would you define the real and imaginary subsets of the complex numbers? The most obvious way …

Nov 9, 2014 · I understand how to solve problems dealing with imaginary numbers, but I don't understand the reason why they exist and what they really do. Could somebody please explain …

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 …