(imaginary number) does (-i)^2 = -1?
That is what I have in my notes but I think it should be +1, by the following reasoning:
(-i)^2=(-sqrt{-1})^2=-(-1)=+1

Am I correct and just made a mistake in my notes, or have I completely misunderstood something? Hope someone with a little more experience can help clarify this. Thanks!

Question

(imaginary number) does (-i)^2 = -1?
That is what I have in my notes but I think it should be +1, by the following reasoning:
(-i)^2=(-sqrt{-1})^2=-(-1)=+1

Am I correct and just made a mistake in my notes, or have I completely misunderstood something? Hope someone with a little more experience can help clarify this. Thanks!

hartnn · Answer

$(-i)^2= (-1)^2i^2 = 1 (-1)=-1$

hartnn · Answer

from your way, 
(-sqrt{-1})^2 = (-1)^2 * (sqrt{-1})^2 = 1 * (-1) = -1

nikolas · Answer

Ah, can't believe I missed separating the (-1). Thanks for your help!

hartnn · Answer

welcome ^_^