-1 = 1??? why not?

right watch this:
SQRT(1)=1
Thus SQRT(1*1)=1
Thus SQRT(-1*-1)=1
theorem: SQRT(a*b)=SQRT(a)*SQRT(b)
Thus SQRT(-1)*SQRT(-1)=1
Theorem: SQRT(-1)=i where i*i=-1 (i for imaginary)
Thus -1=1

Something is wrong. Where?

>>12
And no, breaking up a negative root into its positive and imaginary part is not complicated, but breaking a positive root into two negative roots (as in the OP's fallacy) IS complicated,  because it arises as a special case of complex square roots, and taking roots of complex numbers is extremely complicated because you need to take a complex log, multiply it by 1/2 and take the complex exponential. Take a course on complex analysis to see how it's done.