I know something is wrong in the following proofs.Can't figure out which step is wrong.
Proof of -1 =1:
Proof of 1=3:
383for 2nd one (2) step
Soumyabrata Mondal log(-1) is not possible 
2305@Soumyabrata Mondal
Even I had thought of that before.
But you see,
\dpi{200} \fn_cs e^{i\pi} = -1\Rightarrow log(-1) = i\pi
Hence log(-1) does have a value.
Soumyabrata Mondal i(pi) is nt real. i is an imaginary number. Shaswata Roy Doesn't matter if it is not real...as long as it is some value which can be cancelled from both the sides.Shaswata Roy Actually I had seen this on a post given by a Singaporean olympiad trainer.He said that log of a negative no. can be taken.Shaswata Roy All I know is that the answer has got something to do with the property of log (or antilog don't know,:P) and it has got something to do with one to one correspondence or something like that.Soumyabrata Mondal ok, then I think it is out of my knowledge :-(
229For 1st one.....
The first question was given in ISI
you cant express two negative nos which are in square root
form as two different roots...i mean√(-1*-1) cannot be written as root-1 *root -1...nd @Roy the question is --"Proof that"?? :-|
Shaswata Roy Obviously "proof that" cos I am not asking anyone 2 prove anything.It's a "proof" that -1=1 and 1=3.Shaswata Roy By the way,thanks for finding out the flaw.Dwijaraj Paul Chowdhury ;-)36√ (-1).(-1) equals 1
Shaswata Roy Not necessarily....it can be -1 too.Soumyabrata Mondal how??229for the 1st proof
Dekh log er value replace korle
3i*pi=1i*pi
Now LHS=(0,3*pi)
And RHS=(0,pi) by multiplication of complex nos. But as they don't represent the same complex nos. on an argand plane, they cannot be equal. :. Contradiction. LHS is not equal to RHS.
Shaswata Roy Thanks for stating the obvious :P....It's known that LHS is not equal 2 RHS . I am asking why they are not equal (i.e. what mistake had I made while taking the log).As I had said b4 2 Soumyabrata, it has got something 2 do with one to one correspondence property of log or something like that(don't know).
337I think, for the 2nd one,
log is not possible for a negative number.
