document.write( "Question 162617: i^17 \r
\n" ); document.write( "\n" ); document.write( "the only thing I know about this is that all things like this such as i^30 or i ^2 or i^7 all come up to one thing but I'm not sure what it is \r
\n" ); document.write( "\n" ); document.write( "please help soon!
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Algebra.Com's Answer #119827 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Evaluate:
\n" ); document.write( " $\"i%5E17\"$
\n" ); document.write( "Recall that:
\n" ); document.write( " $\"i%5E1+=+%28sqrt%28-1%29%29%5E1\"$ = $\"i\"$
\n" ); document.write( " $\"i%5E2+=+%28sqrt%28-1%29%29%5E2\"$ = $\"-1\"$
\n" ); document.write( " $\"i%5E3+=+%28sqrt%28-1%29%29%5E3\"$ = $\"-1%2Ai+=+-i\"$
\n" ); document.write( " $\"i%5E4+=+%28sqrt%28-1%29%29%5E4\"$ = $\"%28-1%29%5E2+=+1\"$
\n" ); document.write( " $\"i%5E5+=+%28sqrt%28-1%29%29%5E5\"$ = $\"1%2Ai+=+i\"$
\n" ); document.write( "and so on...
\n" ); document.write( "So you can see that the sequence goes:
\n" ); document.write( "i, -1, -i, 1, i, -1, -1, 1,...as the exponent of i goes from:
\n" ); document.write( "1, 2, 3, 4, 5, 6, 7, 8,... every fourth power of i will be = 1, so if you divide the the given exponent of 17 (from $\"i%5E17\"$ ) by 4 you get 4 plus a remainder of 1, so $\"i%5E16+=+1\"$ and $\"i%5E17+=+i\"$ \n" ); document.write( "

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