# SOLUTION: Using DeMoivre's Theorem, find three distinct cube roots of 125

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 Click here to see ALL problems on Trigonometry-basics Question 33174: Using DeMoivre's Theorem, find three distinct cube roots of 125Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!LET N=125=Z^3 SINCE 125^1/3=5...WE CAN WRITE Z^3=(5^3)*1=(5^3){COS(2KPI)+iSIN(2KPI)} SO Z =5*{COS(2KPI)+iSIN(2KPI)}^(1/3) =5*{COS(2KPI/3)+iSIN(2KPI/3)}BY DEMOVIERS THEOREM...PUTTING K=1,2 AND 3 WE GET THE 3 CUBE ROOTS 5*{COS(2*1PI/3)+iSIN(2*1PI/3)}=5(-0.5+i*0.5*SQRT(3))=2.5(-1+i*SQRT(3)) 5*{COS(2*2PI/3)+iSIN(2*2PI/3)}=5(-0.5-i*0.5SQRT(3))= -2.5(1+i*SQRT(3) 5*{COS2*3PI)+iSIN(2*3PI/3)}=5