Miscellaneous - something about the number 'i'

6

Kalyan IIT-K Beware I'm coming ·2010-07-22 06:35:13

what makes you say that 'i' has to be constant??

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49

Subhomoy Bakshi ·2010-07-23 12:39:14

oh ok ok..sorry......

equation specific solution and identity is satisfied for all values of the input, right?(if input is an element of domain set...)

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1

archana anand ·2010-07-23 11:07:50

@shubhomoy
e^iÎ¸=cos Î¸ + i sin Î¸ is not an equation itz an identity....ders difference between the two.

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49

Subhomoy Bakshi ·2010-07-22 15:38:56

kalyan if u call the one u gave as a beautiful equation, then the following one is also an equally but-i-phool equation..:P

(1+2)² = 9 (i say 2, 9 all are constant...so i ask: Is 1 constant? :P)

as i have put x=2 in the equation (1+x)²=1+2x+x²

now the original equation is e^iÎ¸=cos Î¸ + i sin Î¸

here, Î¸ is the variable not i.

i is a constant Imaginary number (i is just a way of writing √-1 in short.)

so, e^iÏ€+1=0 is just a case where u have put Î¸=Ï€

like i had put x=2 in my equation :P ;)

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6

AKHIL ·2010-07-22 10:40:55

arka likes to play with nos..:P

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1

archana anand ·2010-07-22 09:04:55

i see:)

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1

ARKA(REEK) ·2010-07-22 08:56:27

I know Archana ... just tried to put everyone in a maze ... that's all ... hehehe ...

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1

archana anand ·2010-07-22 08:53:11

first question....Is that a equation,when you have angle fixed i.e pi in this case?????
Answer:Itz just the special case of the formula with gives the beautiful identity and not equation.

Second question....Why doesnt this exist????....It actually does.

And i=√-1...so it is constant....(only represented in argand plane though)

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1

ARKA(REEK) ·2010-07-22 08:43:17

I know ... 'i' is a const .... just tried to put in a new theory .....
Like it ... guys .. ??!!

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6

Kalyan IIT-K Beware I'm coming ·2010-07-22 07:49:18

look...tell me any eqaution without variables??can you??if yes then this equation is not beautiful... this equation has all constants...except i which i dont know is constant or not...can u suggest any eqn with only constants and no variables?