User:The Jeff Killer

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

$\ 1=2$

Wikipedia:Babel

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