Linked Questions

1
vote
1answer
2k views

Why Do Imaginary Numbers Exist [duplicate]

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 to me what the point of them ...
-2
votes
3answers
209 views

A polynomial intersecting the x-axis while not intersecting the x-axis?(Complex Numbers) [duplicate]

I know three questions (that gained momentum) that have been posted asking a question which seems the same, but answers to none of them answer the following very well. Please jump to point 2 & 3 ...
3
votes
10answers
116 views

The meaning of i [duplicate]

Can someone kind explain the mathematical quantity i to me (which is the square root of -1)? Just to be clear, I'm not actually trying to understand i per se, I'm just trying to understand how it can ...
2
votes
2answers
113 views

what is the definition of numbers? [duplicate]

Well the question may seem obvious but I can't really find a proper answer to this. Mathematics all seem kind of difficult to understand so please help. I believe it is a quantity. Thanks in advance.i ...
0
votes
1answer
182 views

Imaginary Numbers [duplicate]

Can someone help me by explaining what imaginary numbers actually are, please? I know that it is defined as $i = \sqrt{-1}$ and I can find umpteen sources telling me how to calculate with them but I ...
1
vote
1answer
107 views

Meaning of imaginary number [duplicate]

I'm a bit confused about the true meaning of imaginary number. It's my understanding that a complex number is a number of the form $a+ib$, where $a$ and $b$ are real numbers. A pure imaginary number ...
0
votes
1answer
174 views

What are complex numbers, actually? [duplicate]

What are complex numbers, actually? You can prove $1=-1$ and a complex cosine function can have value greater than $1$ and so on, there are many unexpected results when we use complex numbers. So, ...
-1
votes
1answer
107 views

Why is there root of -1? [duplicate]

Always have we heard that there isn't a root of a negative number. That's why we call the root of -1 an imaginary number. But why, why do we need it and how even did they discover this case? I would ...
-2
votes
1answer
60 views

Square root of -1 [duplicate]

Hello stackexchange users! I am somewhat confused on $\sqrt{-1}$. I believe the answer should be no solution, or inconsistent, or at least something in that nature. Am I correct or am I most likely ...
1
vote
1answer
84 views

What is the mathematical nature of $i$? [duplicate]

It is well known that $i$ is unit imaginary part of any complex number, but many uses of $i$ show that has others mathematical properties, for example in integration area, if I want to compute ...
463
votes
36answers
59k views

Do complex numbers really exist?

Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious ...
60
votes
15answers
7k views

How can I introduce complex numbers to precalculus students?

I teach a precalculus course almost every semester, and over these semesters I've found various things that work quite well. For example, when talking about polynomials and rational functions, in ...
25
votes
8answers
3k views

What's the precise meaning of imaginary number?

The same to the title,what's the precise meaning of imaginary number? And on the other hand,how can the imaginary number be reflected in Physics?
17
votes
5answers
3k views

Can I keep adding more dimensions to complex numbers?

I know about the concept of the complex plane, but is it possible to move to the third dimension? What about arbitrary many dimensions? Edit: could you please give me some examples of 3D numbers?
6
votes
3answers
815 views

How can people understand complex numbers and similar mathematical concepts?

In mathematics, how does something like complex numbers apply to the real world? Why do complex numbers exist? How can we comprehend addition of complex numbers? For example, addition of natural ...

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