Komplexné čísla
(z^3+1).(iz^2+(1+i)z+1)=0
Odpovědi
Diskuze
(z^3+1)*(iz^2+z+iz+1)=0
z^3*(iz^2+z+iz+1)+(iz^2+z+iz+1)=0
(iz^5+z^4+i*z^4+z^3)+(iz^2+z+iz+1)=0
iz^5+z^4+iz^4+z^3+iz^2+z+iz+1=0
z^4+z^3+z+1 + iz^5+iz^4+iz^2+iz=0
z^4+z^3+z+1 + iz(z^4+z^3+z+1)=0
z^4+z^3+z+1 =-iz(z^4+z^3+z+1)
(z^4+z^3+z+1)/(z^4+z^3+z+1) = -iz
-1/i = z
-1/i * i/i= z
i = z
z = i
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(z+1)(z^2-z+1)[iz(z+1)+(z+1)]=(z+1)(z^2-z+1)(z+1)(iz+1)=(z+1)^2(z^2-z+1)(iz+1)
(z+1)^2(z^2-z+1)(iz+1)=0
1) (z+1)^2 = 0 => z=-1
2) z^2-z+1 = 0 => z=(1/2)±(√3/2)i
3) iz+1=0 => z = -1/i *(i/i) = i