If Q is real and z₁, z₂ are connected by z₁^2+z₂^2+2 z₁ z₂ =0 , then triangle with vertices 0, z₁ and z₂ is

Step-by-step solution

z₁^2+z₂^2+2 z₁ z₂ =0 ( z₁ z₂ )^2+2 ( z₁ z₂ ) +1=0 ( z₁ z₂ + )^2=- (1- ^2 )=- ^2 z₁ z₂ =- i | z₁ z₂ |= (- )^2+( )^2 =1 array lrl & |z₁ |= |z₂ | & |z₁-0 |= |z₂-0 | array Thus, triangle with vertices 0, z₁, z₂ is iscosceles.