document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #652374 by Theo(13342) $\"\"$ $\"About$

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i is equal to the square root of -1.
\n" ); document.write( "if you have just reached a pure imaginary number, then you have reached a number that is the square root of a negative number.
\n" ); document.write( "if you multiply that number by i, then you get the square root of a negative number times the square of -1.
\n" ); document.write( "this is equal to the square root of the (negative number * -1) which becomes the square root of a positive number which is possible.
\n" ); document.write( "i have no idea how you could possible dial an imaginary number, bus assuming you could, then .......
\n" ); document.write( "assume you dialed sqrt(-4).
\n" ); document.write( "that's an imaginary number.
\n" ); document.write( "when you multiply that number by i, you are multiplying it by sqrt(-1).
\n" ); document.write( "you get sqrt(-4) * sqrt(-1) which is equal to sqrt(-4 * -1) which is equal to sqrt(4) which is equal to 2.
\n" ); document.write( "in fact, the sqrt(-4) is equal to sqrt(4)*i which is then equal to 2i.
\n" ); document.write( "the joke is just a take off on how imaginary numbers are displayed, as far as i can tell.\r
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