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##### why i square is equal to -1 but not 1???

I’m just wondering that the imaginary number i is √-1 and so i square would be (√-1)(√-1) and equals to -1 But if calculate like √-1*(-1) then it would be √1 and equals to 1 I know the right answer is -1 but why is the second one wrong? Is it just forbidden to calculate like this or there are other explanations?

##### now the ADVANCED math Limerick version: ∫3√31t2dt⋅cos(3π9)=ln(e√3) Integral t squared dt, from 1 to the cube root of 3, times the cosine, of three pi over 9, equals log of the cube root of e.

now the ADVANCED math Limerick version: ∫3√31t2dt⋅cos(3π9)=ln(e√3) Integral t squared dt, from 1 to the cube root of 3, times the cosine, of three pi over 9, equals log of the cube root of e.

##### ELI5: why i square is equal to -1 but not 1???

I’m just wondering that the imaginary number i is √-1 and so i square would be (√-1)(√-1) and equals to -1 But if calculate like √-1*(-1) then it would be √1 and equals to 1 I know the right answer is -1 but why is the second one wrong? Is it just forbidden to calculate like this or there are other explanations?

##### why isn't the area under xy=1 equal to 2 square units?

We can draw a line, x=y intersecting the curve xy=1 at (1,1)
we can now compute the integrals with respect to the x and y axis and hence get the area to be 2 square units

why is this wrong?

##### [LifeProTips] LPT: For homeowners doing their own electrical work: When replacing sockets and switches (ESPECIALLY a lot of them), use a #1 square driver bit instead of a flat-head or Phillips; it's MUCH easier, and will allow you to achieve a tighter connection with less effort.         