User:The Jeff Killer

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[edit] Math

  • Everyone knows this:

\frac{-1}{1}= \frac{1}{-1}

  • Now we will square root both sides:

\sqrt{\frac{-1}{1}}= \sqrt{\frac{1}{-1}}

  • Now we break up the roots:

\frac{\sqrt{-1}}{\sqrt{1}}= \frac{\sqrt{1}}{\sqrt{-1}}

  • The square root of a negative 1 is i and the square root of 1 is 1. In other words:

\frac{i}{1} = \frac{1}{i}

  • Now we multiply the entire thing by 1/2:

\frac{i}{2} = \frac{1}{2i}

  • Now let's add 3/(2i) to this to make the math easier.

\frac{i}{2} + \frac{3}{2i} = \frac{1}{2i} + \frac{3}{2i}

  • Now we can multiply the entire thing by i:

i(\frac{i}{2} + \frac{3}{2i}) = i(\frac{1}{2i} + \frac{3}{2i})

  • So now we expand this beast:

\frac{i^2}{2} + \frac{3i}{2i} = \frac{i}{2i} + \frac{3i}{2i}

  • We know that the square root of -1 is i, so i^2 must be -1.:

\frac{-1}{2} + \frac{3i}{2i} = \frac{i}{2i} + \frac{3i}{2i}

  • Now we simplify the i's

\frac{-1}{2} + \frac{3}{2} = \frac{1}{2} + \frac{3}{2}

  • Let's calculate this thing:

\frac{2}{2} = \frac{4}{2}

  • And so

\ 1 = 2

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