Tuesday, September 28, 2010

To prove 1+1 = 0

we all know that 1+1 =2 but using compelex numbers like i which is equal to root of -1 we can prove 1+1 = 0


let

1 + 1 = 1 + √1

as we can take the value of √1 for 1

= 1 + √-1 * -1

because -1 * -1 is + 1

= 1 + √-1 * √ -1

now we can separate the multipliers and finally as we can denote √-1 with complex charecter i

then


= 1 + i * i

which can be written with squares like this


= 1 + i²

as we know that i = √-1

and (√a)² is a with it we can write it like this now


= 1 + (√-1)²

= 1 + (-1)

as + * - is -

= 1 - 1

= 0


this is how we can prove 1 + 1 = 0 and usign the prvious method of proofs given in previous posts also we can prove it but this is a different style of proof
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