Re: 1 = -1 math puzzle

Where is the mistake?

1 =
sqrt (1) =
sqrt (-1*-1) =
sqrt(-1) * sqrt(-1) =
i * i =
-1

In line 3, when you went from the line of
real numbers to the complex numbers. The
complex quantities you are actually multiplying
are 0+sqrt(-1)*0+sqrt(-1), which signifies
that the real part of the complex number is
0 (not 1). Multiplying the quantities, as
you find, results in another real number, -1.

In fact, it is because of this rotation of
points in the complex plane about the point
of origin that makes imaginary numbers so useful
for real world applications--equations that would be
impossible to solve in ordinary terms (like
x^2=-1, the puzzle that started the whole thing
long ago)are easily dealt with in the complex plane.

If you want a good popular book on how and why
complex numbers work, and the history of their
development, I recommend Barry Mazur's Imagining
Numbers.

Tom
.