Richard Lee
Member
Since i^2=-1, therefore, i=(+/-)sqrt(-1). Becareful, it's wrong!
-
Finished your HSC? Check out our University Discussion, Non-School forums or help out next year's HSC students! -
YOU can help the next generation of students in the community! Share your trial papers and notes on our Notes & Resources page
Easy qn2 (1 Viewer)
- Thread starter Richard Lee
- Start date
N
ND
Guest
Where's the question? i is defined as sqrt(-1). Also, think of the argand plane, i is only positive.
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" ?
"9 = 9 OR 9 = 0" ?
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?
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?
KeypadSDM
B4nn3d
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.
:. (+-)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.
Last edited: