Question

z^4+4=0 на множестве комплексных

Answer 1

z^4+4=0; 

z^4+4z^2-4z^2+4=0;

(z^4+4z^2+4)-4z^2=0;

(z^2+2)^2-(2z)^2=0;

(z^2-2z+2)(z^2+2z+2)=0; 

 

z^2-2z+2=0 V z^2+2z+2=0;

 

z^2-2z+2=0;

D=4-8=-4

z1=(2+2i)/2=1+i;

z1=1-i

 

z^2+2z+2=0;

D=4-8=-4

z3=(-2+2i)/2=-1+i;

z4=-1-i