document.write( "Question 987127: When z = (1+i)/(1-i), prove that z+z²+z³+z⁴=0 \n" ); document.write( "

Algebra.Com's Answer #607912 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "z+z²+z³+z⁴ = i+i²+i³+i⁴ = i+(-1)+(i²×i)+(i²×i²) = i-1+(-1×i)+(-1×-1) =\r\n" );
document.write( "\r\n" );
document.write( "i-1-i+1 = 0\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );