Linked Questions

2
votes
2answers
3k views

Prove $e^{i \pi} = -1$ [duplicate]

Possible Duplicate: How to prove Euler's formula: $\exp(i t)=\cos(t)+i\sin(t)$ ? I recently heard that $e^{i \pi} = -1$. WolframAlpha confirmed this for me, however, I don't see how this ...
10
votes
2answers
3k views

Intuition behind euler's formula [duplicate]

Possible Duplicate: How to prove Euler's formula: $\\exp(i t)=\\cos(t)+i\\sin(t)$ ? Hi, I've been curious for quite a long time whether it is actually possible to have an intuitive ...
0
votes
1answer
794 views

Why Euler's formula is true? [duplicate]

Possible Duplicate: How to prove Euler’s formula: $\exp(i t)=\cos(t)+i\sin(t)$? I need to know why Euler's formula is true? I mean why is the following true: $$ e^{ix} = \cos(x) + i\sin(x) $$
2
votes
1answer
167 views

Where does this equation come from? [duplicate]

Since I study 3 years i ask myself very often where does this equation come from? $$e^{i\theta} = \cos(\theta)+i \sin(\theta)$$ Is it found by series expansion?
-2
votes
2answers
693 views

Why is $sinx$ the imaginary part of $e^{ix}$? [duplicate]

Most of us who are studying mathematics are familiar with the famous $e^{ix}=cos(x)+isin(x)$. Why is it that we have $e^{ix}=cos(x)+isin(x)$ and not $e^{ix}=sin(x)+icos(x)$? I haven't studied Complex ...
3
votes
3answers
220 views

What is the meaning of Euler's identity? [duplicate]

I know that euler's identity state that $e^{ix} = \cos x + i\sin x$ But e is a real number. What does it even mean to raise a real number to an imaginary power. I mean multiplying it with itself ...
0
votes
1answer
261 views

What is the most intuitive explanation for euler's identity? [duplicate]

Is there any intuitive explanation for: $$e^{i\pi} + 1 = 0$$ About whether this question is a duplicate, what is asked for is not a proof but an explanation that helps with the not-so-intuitive ...
4
votes
1answer
114 views

How to determine if a $\lim\limits_{n \rightarrow \infty}{(1+{ix\over n})^n}$ would be complex [duplicate]

Question Recently, I have been looking at complex limits, The most famous being $e^{ix}$=$\lim\limits_{n \rightarrow \infty}{(1+{ix\over n})^n}$. An example would be that when $x = \pi$ we know that ...
0
votes
4answers
397 views

Why does $e^{i\pi}=-1$? [duplicate]

I will first say that I fully understand how to prove this equation from the use of power series, what I am interested in though is why $e$ and $\pi$ should be linked like they are. As far as I know $...
0
votes
1answer
68 views

Exponential Form of Complex Numbers - Why e? [duplicate]

Please delete this question please. It is a duplicate. Thank you!!!!!! I cannot delete the question. Thanks!
1
vote
1answer
39 views

What is the value of $e^{3i \pi /2}$? [duplicate]

When solving for the value, we know that $e^{\pi i}=-1$ . I am confused as to what is the right answer when you evaluate this.I am getting two possible answers: $e^{3\pi i/2}$ = $(e^{\pi i})^{3/2}$ so ...
114
votes
40answers
54k views

Why is negative times negative = positive?

Someone recently asked me why a negative $\times$ a negative is positive, and why a negative $\times$ a positive is negative, etc. I went ahead and gave them a proof by contradiction like so: Assume ...
66
votes
14answers
4k views

Pseudo Proofs that are intuitively reasonable

What are nice "proofs" of true facts that are not really rigorous but give the right answer and still make sense on some level? Personally, I consider them to be guilty pleasures. Here are examples ...
27
votes
8answers
3k views

Why is uniqueness important for PDEs?

Every text on PDEs I come across will spend alot of time on showing the existence and uniqueness of solutions to a particular PDE. The importance of the existence of a solution to a PDE is obvious, ...
27
votes
9answers
3k views

What does it mean to represent a number in term of a $2\times2$ matrix?

Today my friend showed me that the imaginary number can be represented in term of a matrix $$i = \pmatrix{0&-1\\1&0}$$ This was very very confusing for me because I have never thought of it ...

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