Question

Sa se rezolve in multimea nr complexe ecuatia

Answer 1

Inmultesti  egalitatea  cu  (z+1).Dupa  efectuarea  inmultirilor  si  reducerii  termenilor  opusi  vei  obtine
z^7+1=0  z^7=-1 scrii  numarul sub  forma  trigonometrica
z^7=cosπ+isinπ  Observi  ca l z^7l=1
Aplici  formula
Zk=cos (π+2kπ)/7+isin(π+2kπ)/7  k={0,1,2...6}
zo=cosπ/7+isinπ/7
z1=cos(π+2π)/7+isin(π+2π)/7=cos3π/7+isin3π/7
z2=cos(π+4π)/7+i sin(π+4π)/7=cos5π/7+isin5π/7
z3=cos(π+6π)/7+isin(π+6π)/7=cos π+isinπ
..........................................................................
z6=cos(π+12π)+isin(π+12π)/7=cos13π/7+isin13π/7