document.write( "Question 33174: Using DeMoivre's Theorem, find three distinct cube roots of 125 \n" ); document.write( "

Algebra.Com's Answer #19632 by venugopalramana(3286) $\"\"$ $\"About$

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LET N=125=Z^3
\n" ); document.write( "SINCE 125^1/3=5...WE CAN WRITE Z^3=(5^3)*1=(5^3){COS(2KPI)+iSIN(2KPI)}
\n" ); document.write( "SO Z =5*{COS(2KPI)+iSIN(2KPI)}^(1/3)
\n" ); document.write( "=5*{COS(2KPI/3)+iSIN(2KPI/3)}BY DEMOVIERS THEOREM...PUTTING K=1,2 AND 3 WE GET THE 3 CUBE ROOTS
\n" ); document.write( "5*{COS(2*1PI/3)+iSIN(2*1PI/3)}=5(-0.5+i*0.5*SQRT(3))=2.5(-1+i*SQRT(3))
\n" ); document.write( "5*{COS(2*2PI/3)+iSIN(2*2PI/3)}=5(-0.5-i*0.5SQRT(3))= -2.5(1+i*SQRT(3)
\n" ); document.write( "5*{COS2*3PI)+iSIN(2*3PI/3)}=5 \n" ); document.write( "

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