document.write( "Question 79349: $\"i%5E1=+i\"$ $\"+i%5E5+=+i\"$
\n" ); document.write( " $\"i%5E2=+-1+\"$ $\"+i%5E6+=+-1\"$
\n" ); document.write( " $\"i%5E3=+-i+\"$ $\"++i%5E7=+-i\"$
\n" ); document.write( " $\"i%5E4=+1+\"$ $\"+i%5E8+=+1\"$ \r
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\n" ); document.write( "\n" ); document.write( "I am supposed to use the above pattern to simplify the powers of i.\r
\n" ); document.write( "\n" ); document.write( " $\"i%5E65\"$ \r
\n" ); document.write( "\n" ); document.write( "Please help
\n" ); document.write( "Please help \n" ); document.write( "

Algebra.Com's Answer #56949 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"i%5E1=+i\"$ $\"+i%5E5+=+i\"$
\n" ); document.write( " $\"i%5E2=+-1+\"$ $\"+i%5E6+=+-1\"$
\n" ); document.write( " $\"i%5E3=+-i+\"$ $\"++i%5E7=+-i\"$
\n" ); document.write( " $\"i%5E4=+1+\"$ $\"+i%5E8+=+1\"$
\n" ); document.write( "The easiest property to make use of is
\n" ); document.write( " $\"i%5E4=+1+\"$ because every time you
\n" ); document.write( "multiply it times itself, you still get 1
\n" ); document.write( " $\"i%5E4+%2A+i%5E4+=+1\"$
\n" ); document.write( " $\"i%5E4+%2A+i%5E4+%2A+i%5E4+=+1\"$
\n" ); document.write( " $\"i%5E4+%2A+i%5E4+%2A+i%5E4+%2A+i%5E4+=+1\"$
\n" ); document.write( "Remember you ADD the exponents in each case, so
\n" ); document.write( " $\"i%5E8+=+1\"$
\n" ); document.write( " $\"i%5E12+=+1\"$
\n" ); document.write( " $\"1%5E16+=+1\"$
\n" ); document.write( "Think of $\"i%5E65\"$ as $\"i%5E4\"$ multiplied times itself a certain
\n" ); document.write( "number of times and multiply that by whatever factor is left over
\n" ); document.write( " $\"65%2F4+=+16\"$ and 1 remainder
\n" ); document.write( "What you've got is $\"%28i%5E4%29%5E16+%2A+i\"$ or
\n" ); document.write( " $\"1%5E16+%2A+i+=+i\"$
\n" ); document.write( "So, $\"i%5E65+=+i\"$ answer \n" ); document.write( "

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