Help me calculate corner frequencies

[ElectricDruid]

The square root of -1 is not the same as the imaginary unit (i or j) because the square root of -1 is j and

Sorry, what?

I thought i and j were both the imaginary unit and defined as the square root of -1.

If i x i = -1, then it's pretty clear that -i x -i also = -1.

Tom

[EBK]

The square root of -1 is not the same as the imaginary unit (i or j) because the square root of -1 is j and

Sorry, what?

I thought i and j were both the imaginary unit and defined as the square root of -1.

If i x i = -1, then it's pretty clear that -i x -i also = -1.

Tom

I was thrown by that too, but....
i (or j) is _a_ square root of -1. 

Think about it this way:
i × i = -1
and
(-i) × (-i) = -1Edit: Sorry, Tom, you already said that.

It's sort of like saying 2 and -2 are each a square root of 4.

I guess it might be more accurate to say we replace sqrt(-1) with i (or j).   

[antonis]

Peace brothers... 

Szabolcs is partially right (although wrong in strictly math terms)  because, in practice, there isn't any case in which we can meet j or -j standing alone..
(i.e as a constant added to or subtracted from the variable part of a function..)

It always appears as numerator/denominator of a fraction or as a coefficient of a magnitude (constant or variable) so we use its absolute value for algebraic sums..
i.e. capacitive rectance of a capacitor is X_C = -j/ωfC but we shouldn't mind if it was X_C =  j/ωfC.   

P.S.
Vector/phasor values is anothewr matter..