document.write( "Question 1181163: If 1 and w are 2 of the 5 roots of (w)^5 = 1, then prove the following:\r
\n" ); document.write( "\n" ); document.write( "a) (w)^2, (w)^3, and (w)^4 are the remaining roots of (w)^5 = 1\r
\n" ); document.write( "\n" ); document.write( "b) 1 + w + (w)^2 + (w)^3 + (w)^4 = 0\r
\n" ); document.write( "\n" ); document.write( "c) (w)^(5n) = 1 for any integer n \n" ); document.write( "

Algebra.Com's Answer #811039 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
If 1 and w are 2 of the 5 roots of (w)^5 = 1, then prove the following:
\n" ); document.write( "a) (w)^2, (w)^3, and (w)^4 are the remaining roots of (w)^5 = 1
\n" ); document.write( "

\r\n" );
document.write( "where cis(θ) = cos(θ)+isin(θ),\r\n" );
document.write( "The 5 fifth roots of 1 are \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "

b) 1 + w + (w)^2 + (w)^3 + (w)^4 = 0, provided w ≠ 1

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since w ≠ 1, w-1 ≠ 0, so\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "

c) (w)^5n = 1 for any integer n

\r\n" );
document.write( "\r\n" );
document.write( "Raise both sides to the 5th power:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );