Easy qn2 (1 Viewer)

[Richard Lee]

Since i^2=-1, therefore, i=(+/-)sqrt(-1). Becareful, it's wrong!

 

[ND]

Where's the question? i is defined as sqrt(-1). Also, think of the argand plane, i is only positive.

 

[wogboy]

Technically it is a correct (true) statement, because saying i = (+/-) sqrt(-1) is logically equivalent to saying i = sqrt(-1) OR i = - sqrt(-1) (note the OR). There is one true statement and one false statement. As you know from logic true OR false, is true. Is the following statement correct:

"9 = 9 OR 9 = 0" ?

 

[sammeh]

consider:

if i = +/-[(sqrt)-1]

when i = +[(sqrt)-1], i^2 = -1
therefore when i = -[(sqrt)-1], i^2 = 1

....which is obviously incorrect.

the basis of the +/- statement concerning roots is that there are 2 solutions, which give the same value regardless of the sign. this is not applicable in the case of i. so, really its meaningless and therefore unneccesary to define i as +/-(sqrt)-1.

wow that sounds really really condescending, and im probly not even right, but as far as my reasoning goes, im pretty sure i am. yes/no/feedback?

 

[wogboy]

Sounds good to me. That's a proof by contradiction that i =/= - sqrt(-1).

 

[KeypadSDM]

9 = 3^2

:. (+-)3 = 3

Same thing as above, you can't legitimately do this as you've performed 2 different operations on either side.

On the right you've taken the positive square root, and on the left you've taken both square roots.