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### 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 ...
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### 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 ...
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### 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: $$e^{ix} = \cos(x) + i\sin(x)$$
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 $... 1answer 68 views ### Exponential Form of Complex Numbers - Why e? [duplicate] Please delete this question please. It is a duplicate. Thank you!!!!!! I cannot delete the question. Thanks! 1answer 39 views ### What is the value of$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}$so ... 40answers 54k views ### Why is negative times negative = positive? Someone recently asked me why a negative$\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 ... 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 ... 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, ... 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 ...