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Question Number 124320 by sogol last updated on 02/Dec/20

z+(1/z)=1 z^3 =??

z+1z=1z3=??

Answered by Dwaipayan Shikari last updated on 02/Dec/20

z^2 −z+1=0⇒z=((1±i(√3))/2)=e^(±((iπ)/3)) z^3 =e^(±iπ) =−1

z2−z+1=0⇒z=1±i32=e±iπ3z3=e±iπ=−1

Answered by $@y@m last updated on 02/Dec/20

(z+(1/z))^3 =1^3 z^3 +(1/z^3 )+3(z+(1/z))=1 z^3 +(1/z^3 )+3=1 z^3 +(1/z^3 )+2=0 (z^3 )^2 +2z^3 +1=0 (z^3 +1)^2 =0 z^3 =−1

(z+1z)3=13z3+1z3+3(z+1z)=1z3+1z3+3=1z3+1z3+2=0(z3)2+2z3+1=0(z3+1)2=0z3=−1

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