- #1
LHarriger
- 69
- 0
Imaninary numbers, i=1 ??!
Ok, this is driving me crazy:
[itex]i^{2}=-1[/itex]
no problem here, but
[itex]i^{2}=\left(\sqrt{-1}\right)^{2}=\sqrt{(-1)^{2}}=\sqrt{1}=1[/itex]
oops...
I know that the error has to be in this step:
[itex]\left(\sqrt{-1}\right)^{2}=\sqrt{(-1)^{2}}[/itex]
(works fine for positive numbers)
and I am pretty sure it has something to do with principle roots.
However, I just can't figure out a clean argument for what exactly is wrong.
Please help!
Ok, this is driving me crazy:
[itex]i^{2}=-1[/itex]
no problem here, but
[itex]i^{2}=\left(\sqrt{-1}\right)^{2}=\sqrt{(-1)^{2}}=\sqrt{1}=1[/itex]
oops...
I know that the error has to be in this step:
[itex]\left(\sqrt{-1}\right)^{2}=\sqrt{(-1)^{2}}[/itex]
(works fine for positive numbers)
and I am pretty sure it has something to do with principle roots.
However, I just can't figure out a clean argument for what exactly is wrong.
Please help!