## e^ipi + 1 = 0

For college and university level advanced Mathematics
Dipan
Posts: 158
Joined: Wed Dec 08, 2010 5:36 pm

### e^ipi + 1 = 0

In a book I have got that ,
e^i pi = cos pi + i sin pi.
but how?????

AntiviruShahriar
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### Re: e^ipi + 1 = 0

"College / University Level" e r 1ta post kora ache..oita poira dekho.....post name "\$i^i\$"

tanvirab
Posts: 446
Joined: Tue Dec 07, 2010 2:08 am

### Re: e^ipi + 1 = 0

Do you know about Taylor series? The Taylor series for exponential function can be generalized to complex numbers. Then it's just a matter of writing it as the sum of the Taylor series of cosine and the Taylor series of sine (multiplied by \$i\$).

tanvirab
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### Re: e^ipi + 1 = 0

Dipan
Posts: 158
Joined: Wed Dec 08, 2010 5:36 pm

### Re: e^ipi + 1 = 0

@Anti...tomar divisional mo te ki asche...

tanvirab
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### Re: e^ipi + 1 = 0

abir91
Posts: 52
Joined: Sun Dec 19, 2010 11:48 am

### Re: e^ipi + 1 = 0

Note that, dealing with infinity without understanding Analysis properly can lead to nasty disasters. So although the proof is correct, I think one will appreciate the result properly when he can fill the gaps. If you can't, for the time being, just remember that there are things that needs to be proved before you can prove it.

*If you are familiar with analysis, then ignore my comment.
Abir

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Dipan
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Joined: Wed Dec 08, 2010 5:36 pm

### Re: e^ipi + 1 = 0

@Abir bhai...Have you told this to me?I can't understand what you wanted to say..Please, make it clear to me..

abir91
Posts: 52
Joined: Sun Dec 19, 2010 11:48 am

### Re: e^ipi + 1 = 0

No. It was intended for a general audience, not necessarily only you.

I meant there are gaps in that proof which needs to proved (the author did not include them is because he assumed the audience knows them), but if you don't see them right now, don't worry, just know that there are gaps and you will prove them later when you learn how to treat these things rigorously.
Abir

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tanvirab
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