Question

Fie x1 si x2 radacinile ecuatiei x^2+2x+2=0. Sa se arate ca x1^4=x2^4

Answer 1

delta=2^2-2*4=-4

x1=(-2+2i):2=-1+i

x2=(-2-2i):2=-1-i

x1^4=(-1+i)^2*(-1+i)^2=(1-2i+i^2)*(1-2i+i^2)=(1-2i-1)*(1-2i-1)=(-2i)*(-2i)=4i^2=-4

x2^4=(-1-i)^2*(-1-i)^2=(1+2i+i^2)*(1+2i+i^2)=(1+2i-1)*(1+2i-1)=2i*2i=4i^2=-4

=> x1^4=x2^4