Question

x=-1/x

Answer 1

x=-1/x


x*x = -1


x^2 = -1


x = +-sqrt(-1)


x = sqrt(-1) or x = -sqrt(-1)


x = i or x = -i


Note: i = sqrt(-1)

Answer 2

but if i is positive
i=-1/i
i=-1/i
a positive number equals a negative number

~

or if i is negative . a negative number equals a positive number
-1=-1/-i
-1=1/i

Answer 3

is sqrt(-1) positive or negative
/?

Answer 4

if x = i, then


x = -1/x

i = -1/i

i = (-1/i)*(i/i)

i = -i/(i^2)

i = -i/(-1)

i = i


So this confirms that x = i is a solution


Do the same for x = -i to confirm it is indeed a solution

Answer 5

if x = -i, then
x = -1 / x
-i = -1 / -i
-i = (-1 / -i)*(-i/-i)
-i = i / i^2
-i = 1/i

Answer 6

-i = i/-1 = -i

Answer 7

so i is neither positive negative or zero,
how can this be the real solution?

Answer 8

close, but your last line should be

-i = i / (-1)


which then becomes


-i = -i


which confirms x = -i as a solution as well

Answer 9

oh you fixed it, nvm

Answer 10

i is the square root of negative 1, it is not a real number

Answer 11

is it kinda 'half negative'?

Answer 12

what? the value of i?

Answer 13

yeah the value of i seams to be between negative and neutral

Answer 14

well i don't think it's valid to think of i as positive or negative since that applies to real numbers only

Answer 15

ok

Answer 16

\[x=-\frac{1}{x}\]
\[x^2=-1\]
\[x=\pm i\]