Question

Rezolvati ecuatia:
Z la puterea 3=(1+i)/(1-i)

Answer 1

Răspuns:

Explicație pas cu pas:

z³=(1+i)²/(1-i²)=2i/2=i=cosπ/2+isinπ/2

z1,2,3=cos((π/2+2kπ)/3) +isin ((π/2+2kπ)/3)

z1=cosπ/6+isinπ/6=√3/2+i/2

z2=cos(5π/6)+isin(5π/6)=-√3/2+i/2

z3=cos(9π/6)+isin(9π/6)=cos(2π/3)+isin(2π/3)=-1/2-i√3/2