Tagged Questions
1
vote
1answer
41 views
What is the modulus of a number?
What is the exact definition of the modulus of a number? As far as I know, it is the distance between the origin and the point associated with this number. So if $z=a+bi \in \Bbb ...
0
votes
0answers
106 views
What is the correct definition for an imaginary number?
The following is taken from Wikipedia's definition.
An imaginary number is a number whose square is less than or equal to
zero.
But I also heard that
An imaginary number is a number whose ...
20
votes
5answers
803 views
Is the square root of -1 rational?
This is not a deep question, but if there is a definite answer then here is the place where I will find it.
Is it justified to say that $i =\sqrt{-1}$ is rational?
The origin of this question lies ...
5
votes
1answer
145 views
Why do Quaternions and octonions exist?
Ok so I have known about imaginary numbers for quite some time now. I also understand why we want them to exist (to have a solution for $x^2=-1$). I also remember reading that the complex numbers are ...
3
votes
2answers
146 views
What is the proper name for this number system?
The FractInt documentation makes mention of two number systems which extend the complex numbers: the "quaternions" and the "hypercomplex numbers".
However, Wikipedia claims that "hypercomplex number" ...
4
votes
1answer
305 views
Why are imaginary numbers called imaginary numbers
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 "imaginary"?
0
votes
1answer
103 views
terminology: euler form and trigonometric form
Am I right, that the following is the so-called trigonometric form of the complex number $c \in \mathbb{C}$?
$|c| \cdot (\cos \alpha + \mathbf{i} \sin \alpha)$
And the following is the Euler form of ...
7
votes
1answer
260 views
Why is $i$ called “imaginary”?
I was reading this question, and, after reading the responses, I felt like I had a much better understanding about how they're just another type of number definition.
Why, then, are they called ...
15
votes
5answers
1k views
How fundamental is the fundamental theorem of algebra?
Despite its name, its often claimed that the fundamental theorem of algebra (which shows that the Complex numbers are algebraically closed - this is not to be confused with the claim that a polynomial ...
