Is $1= -1$ ?
because, $1=\sqrt{1}
=\sqrt{-1×-1}
=\sqrt{-1}×\sqrt{-1 }
= i×i
= i^2 = -1 $
this can be done with all natural numbers. how this can be? please help me
Asked
Active
Viewed 33 times
-1
CY Aries
- 23,393
-
2"this can be done with all natural numbers" but it can't be done with negative numbers. Or complex numbers. Just forget it. $\sqrt{a\times b} \ne \sqrt a \times \sqrt b$. It doesn't. And if you think about it, no-one one actually ever said it was. We all all just assumed it was okay. – fleablood Apr 04 '18 at 05:29
-
@MuhammedHaleem Please remember that you can choose an answer among the given if the OP is solved, more details here https://meta.stackexchange.com/questions/5234/how-does-accepting-an-answer-work – user Apr 07 '18 at 19:54
1 Answers
0
On complex number this step is wrong
$$1=\sqrt{1}$$
since $\sqrt{1}=(e^{2\pi i})^{\frac12}\pm 1$ and also this one
$$\sqrt{-1}=i$$
since $\sqrt{-1}=(e^{\pi i})^{\frac12}=\pm i$.
user
- 154,566