Let vertices of an acute-angled triangle are `A(z_1),B(z_2),a n dC(z_3)dot` If the origin `O` is he orthocentre of the triangle, then prove that `z_1( bar z )_2+( bar z )_1z_2=z_2( bar z )_3+( bar z )_2z_3=z_3( bar z )_1+( bar z )_(3)z_1`

Let vertices of an acute-angled triangle are A(z_1),B(z_2),a n dC(z_3)dot If the origin O is he orthocentre of the triangle, then prove that z_1( z )_2+( z )_1z_2=_2( z )_3+( z )_2z_3=z_3( z )_1+( z )_(3)z_1dot

Let vertices of an acute-angled triangle are A(z_(1)),B(z_(2)), and C(z_(3))* If the origin O is he orthocentre of the triangle,then prove that z_(1)(bar(z))_(2)+(bar(z))_(1)z_(2)=z_(2)(bar(z))_(3)+(bar(z))_(2)z_(3)=z_(3)(bar(z))_(1)+(bar(z))_(3)z_(1)

Let A(z_1), B(z_2) and C(z_3) forms an acute angled triangle in argand plane having origin as it’s orthocentre. Prove that z_1barz_2+bar(z)_1 z_2=z_2barz_3+barz_2z_3=z_3barz_1 +barz_3z_1

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

If (3+i)(z+bar z)-(2+i) (z- bar z)+14i=0 , then z bar z =

Prove that: R_e z= (z+bar(z))/2, I_m z= (z-bar(z))/(2i) .