Question

Determinati cele 4 radacini complexe ale ecuatiei $z^{4}=i$

Answer 1

Scrii   numarul  sub  forma   trigonometrica
Z^4=cos π/2+isinπ/2
zk=cos(π/2+2kπ)/4+isin(π/2+2kπ)/4     k={0,1,2,3}
zo=cos(π/2)/4+isin(π/2)/4=cosπ/8+isinπ/8
z1=cos(π/2+2π)/4+isin(π/2+2π)/4=cos5π/8+isin5π8
z2=cos(π/2+4π)/4+isin(π/2+4π)/4=cos9π/8+isin9π/8
z3=cos(π/2+6π)/4+isin(π/2+6π)/4=
cos13π/8+isin13π/8