Question

(-1/2 +i√3/2)³+(-1/2-i√3/2)³=?
Trebuie format numarul complex Z=x+iy

Answer 1

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z1=-1/2+i√3/2
lz1l=√(-1./2)²+(√3/2)²=1
cosФ=-1/2 sinФ=√3/2 => Ф=5π/6 cadranul 2
z1=cos 5π/6+isin5π/6
z1³=cos3*5π/6=isin3*5π/6=cos5π/2+isin5π/2=i sin5π2=i
z2=-1/2-i√3/2
lz2l=√1/4+3/4=1
cosФ=-1/2 sinФ=-√3/2=>Ф ∈cadranul3  Ф=4π/3
z2=cos4π/3+isin4π/3
z2³=cos3*4π/3+isin4π/3=cos4π+isin4π=cos4π=1
Z=1+i