why is 1/i = -i, I don't understand how it's -i
can someone explain to me why 1/i = -i
thanks
2007-11-11 21:30:21 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
By definition i² = - 1
1/i = i / i² = i / (-1) = - i
2007-11-12 03:47:05 · answer #1 · answered by Como 7 · 2⤊ 2⤋
Its an imaginary number... what do you expect? Magic happens in the imagination.
i = â[ -1 ]
1 / i = 1 / â[ -1 ]
Simplify that, since we hate radicals in the denominator
1 / i = ( 1 / â[ -1 ] ) â
( i / i )
1 / i = ( 1 / â[ -1 ] ) â
( â[ -1 ]/â[ -1 ] )
1 / i = 1 · â[ -1 ] / â[ -1 ] · â[ -1 ]
1 / i = â[ -1 ] / -1
1 / i = i / -1 = -i
2007-11-12 05:37:03 · answer #2 · answered by Anonymous · 0⤊ 1⤋
i = sq rt (-1)
if you have 1/i and multiply it by i/i. You get i/i^2, which is i/(-1)
or -i.
2007-11-12 05:39:50 · answer #3 · answered by Anonymous · 1⤊ 1⤋
because i^2=-1
that means -i^2=1
if you divide by i you get... what?
2007-11-12 05:34:49 · answer #4 · answered by Theta40 7 · 0⤊ 1⤋