Question

What does \[e^{i\pi}\] mean? What is its significance? Why we have to define such a number?

Answer 1

negative

Answer 2

one

Answer 3

i still don't know why people love it so much. maybe i can't see what they see.

Answer 4

it's basically the relationship of the three constants.

Answer 5

e, iota and pi

Answer 6

Euler's formula

Answer 7

\[e^{i \theta}=\cos \theta +i \sin \theta\]

Answer 8

And the you have it as your pic, without knowing what does it mean?

Answer 9

that is no iota, iota does not have a dot

Answer 10

@Ishaan94 I just think it looked interesting, with 3 special numbers in one term. I knew nothing about it when I uploaded it...

Answer 11

Use @lalaly formula and instead of Theta, substitute pi

you will get -1

Answer 12

hmm \(\sqrt{-1}\) isn't called iota?

Answer 13

but that becomes a complex number

Answer 14

call it i

Answer 15

as in eye, for imaginary

Answer 16

ohh yeah, indian education system sucks or teachers or maybe just me. my life's been a lie. it's not iota! but they made me think it is.

Answer 17

well im sorry to here that but i kinda like the fact the were all Greek for a moment there

Answer 18

iota = root of -1

Answer 19

@Ishaan94 , iota is the greek pronunciation of i

Answer 20

\(\iota\) this 'iota' shivam.

Answer 21

iota is a greek letter(with no dot)... sqrt -1 is i.... as I've learnt..

Answer 22

is*

Answer 23

this is iota and there is no dot on it \[ \iota \]

Answer 24

lol really?

Answer 25

LOLOL The teachers in India have to be tested for their knowledge because they are passing wrong knowledge to us too :(

Answer 26

haha

Answer 27

What is its significance?

Answer 28

See If you multiply a complex number with e^i(Theta) Then the line rotates about angle theta to anticlockwise direction. Diagam below'



|z_2|=|z_1|

Answer 29

Therefore z_2 = z_1 * e^(i(theta))

Answer 30

it means it's too difficult to comprehend

Answer 31

the limit of human intellect

Answer 32

I can see that it would be something interesting...

Answer 33

it means that there's a creator of the universe

Answer 34

Have a look at complex numbers. If you master it , it would make your life and maths and physics problem solving a hell lot easier. :)

Answer 35

i something to do with phase

Answer 36

\( i \quad \iota \quad j\) are some usual notation of the imaginary units. I would never blame my teachers over some notation.

Answer 37

http://isomorphismes.tumblr.com/post/754631763/eipi

Answer 38

@FoolForMath , Ok that brings some clarity to me . Thanks :D
@estudier , an awesome link :D
@everyone, I would say that Euler's law is one of the most important and most useful law I have come across in maths. it makes your life lot easier.

Answer 39

The link helps a lot. Thanks! :)

Answer 40

It's just beautiful, don't ask me why .. it's just is.

Answer 41

Can I ask How? lol hmm -sigh-

Answer 42

e, pi => irrational
i -> not real
when they come to together and form e^( i pi) = -1
-1 is rational and real
irrational + not real -> rational and real => beauty :)