If `z_1, z_2, z_3` are three collinear points in |argand plane, then `|(z_1,bar z_1,1),(z_2,barz_2,1),(z_3,barz_3,1)|=`

If z_1,z_2,z_3 are three collinear points in argand plane, then |[z_1,barz_1,1],[z_2,barz_2,1],[z_3,barz_3,1]|

In complex plane z_(1), z_(2) and z_(3) be three collinear complex numbers, then the value of |(z_(1),barz_(1),1),(z_(2),barz_(2),1),(z_(3), barz_(3),1)| is -

If z_(1) , z_(2) , z_(3) are any three complex numbers on Argand plane, then z_(1)(Im(barz_(2)z_(3)))+z_(2)(Imbarz_(3)z_(1)))+z_(3)(Imbarz_(1)z_(2))) is equal to

If A (z_1), B (z_2) and C (z_3) are three points in the argand plane where |z_1 +z_2|=||z_1-z_2| and |(1-i)z_1+iz_3|=|z_1|+|z_3|-z_1| , where i = sqrt-1 then

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 z_1,z_2,z_3 represent three vertices of an equilateral triangle in argand plane then show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)=0

If z_1,z_2,z_3 are three complex number then prove that z_1Im(barz_2.z_3)+z_2Im(barz_3.z_1)+z_3Im(barz_1.z_2)=0