document.write( "Question 1160400: If 1 and w are two of the five roots of w^5=1, then show that w^2, w^3 and w^4 are the remaining roots of w^5=1. \n" ); document.write( "

Algebra.Com's Answer #783675 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let me start teaching you how to formulate this problem CORRECTLY.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    the number  \" 1 \"   the root of the equation w^5 = 1.\r\n" );
document.write( "\r\n" );
document.write( "    Therefore, there is no need to write  \"if 1 and w are two of the five roots of w^=1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "             (otherwise, it makes very strange impression).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    The correct writing is \"if w is the root of the equation w^5 = 1, different from 1 . . . and so on . . . \".\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now to the solution.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "If w is the root of the equation w^5 = 1, then\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     =  =  =  = 1,\r\n" );
document.write( "\r\n" );
document.write( "    so   is the root of the same equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Same proof works for  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     =  =  =  = 1,\r\n" );
document.write( "\r\n" );
document.write( "    so   is the root of the same equation.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Same proof works for  .\r\n" );
document.write( "\r\n" );
document.write( "Do it on your own, as a useful exercise.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Proved and solved. And completed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );