document.write( "Question 1118051: If 1 and w are two of the five roots of w^(5)=1, then show the following:
\n" ); document.write( "i.w^(2),w^(3), and w^(4) are the remaining roots of w^(5)=1. ii. 1+w+w^(2)+w^(3)+w^(4)=0. iii. w^(5n)=1 for any integer n \n" ); document.write( "

Algebra.Com's Answer #733270 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "i)
\n" ); document.write( " $\"%28w%5E2%29%5E5+=+w%5E10+=+%28w%5E5%29%5E2+=+1%5E2+=+1\"$
\n" ); document.write( " $\"%28w%5E3%29%5E5+=+w%5E15+=+%28w%5E5%29%5E3+=+1%5E3+=+1\"$
\n" ); document.write( " $\"%28w%5E4%29%5E5+=+w%5E20+=+%28w%5E5%29%5E4+=+1%5E4+=+1\"$

\n" ); document.write( "ii)
\n" ); document.write( " $\"1%2Bw%2Bw%5E2%2Bw%5E3%2Bw%5E4+=+%281-w%5E5%29%2F%281-w%29+=+0%2F%281-w%29+=+0\"$

\n" ); document.write( "iii)
\n" ); document.write( " $\"w%5E%285n%29+=+%28w%5E5%29%5En+=+1%5En+=+1\"$
\n" ); document.write( " \n" ); document.write( "

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