Question 1037740: A stand-up comedian uses algebra in some jokes, including one about a telephone recording that announces "You have just reached a pure imaginary number. Please multiply by i and dial again." Explain the joke.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i is equal to the square root of -1.
if you have just reached a pure imaginary number, then you have reached a number that is the square root of a negative number.
if you multiply that number by i, then you get the square root of a negative number times the square of -1.
this is equal to the square root of the (negative number * -1) which becomes the square root of a positive number which is possible.
i have no idea how you could possible dial an imaginary number, bus assuming you could, then .......
assume you dialed sqrt(-4).
that's an imaginary number.
when you multiply that number by i, you are multiplying it by sqrt(-1).
you get sqrt(-4) * sqrt(-1) which is equal to sqrt(-4 * -1) which is equal to sqrt(4) which is equal to 2.
in fact, the sqrt(-4) is equal to sqrt(4)*i which is then equal to 2i.
the joke is just a take off on how imaginary numbers are displayed, as far as i can tell.
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