For any three complex numbers `z_1, z_2 and z_3`, prove that `z_1 lm (bar(z_2) z_3)+ z_2 lm (bar(z_3) z_1) + z_3lm(bar(z_1) z_2)=0`.

For any complex numbers z_(1),z_(2) and z_(3),z_(3)Im(bar(z_(2))z_(3))+z_(2)Im(bar(z_(3))z_(1))+z_(1)Im(bar(z_(1))z_(2)) is

For complex numbers z_1 = 6+3i, z_2=3-I find (z_1)/(z_2)

If z_(1),z_(2),z_(3) are three complex numbers such that 5z_(1)-13z_(2)+8z_(3)=0, then prove that [[z_(1),(bar(z))_(1),1z_(2),(bar(z))_(2),1z_(3),(bar(z))_(3),1]]=0

For any three complex numbers z_(1),z_(2),z_(3) , if Delta=|{:(1,z_(1),bar(z_(1))),(1,z_(2),bar(z_(2))),(1,z_(3),bar(z_(3))):}| , then

For any two non zero complex numbers z_(1) and z_(2) if z_(1)bar(z)_(2)+z_(2)bar(z)_(1)=0 then amp(z_(1))-amp(z_(2)) is

If the triangle fromed by complex numbers z_(1), z_(2) and z_(3) is equilateral then prove that (z_(2) + z_(3) -2z_(1))/(z_(3) - z_(2)) is purely imaginary number

Let z_(1), z_(2), z_(3) be three non-zero complex numbers such that z_(1) bar(z)_(2) = z_(2) bar(z)_(3) = z_(3) bar(z)_(1) , then z_(1), z_(2), z_(3)

Prove that traingle by complex numbers z_(1),z_(2) and z_(3) is equilateral if |z_(1)|=|z_(2)| = |z_(3)| and z_(1) + z_(2) + z_(3)=0