If `z_1` and `z_2` are two complex number such that `|z_1|<1<|z_2|` then prove that `|(1-z_1 bar z_2)/(z_1-z_2)|<1`

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( barz )_2dot

If z_(1)" and "z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 then

It z_(1) and z_(2) are two complex numbers, such that |z_(1)| = |z_(2)| , then is it necessary that z_(1) = z_(2) ?

If z_(1) , z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 and iz_(1)=Kz_(2) , where K in R , then the angle between z_(1)-z_(2) and z_(1)+z_(2) is

Let x_(1)" and "y_(1) be real numbers. If z_(1)" and "z_(2) are complex numbers such that |z_1|=|z_2|=4 , then |x_(1)z_(1)-y_(1)z_(2)|^(2)+|y_(1)z_(1)+x_(1)z_(2)|^(2)=

If z_(1)" and "z_(2) are two complex numbers such that Im(z_(1)+z_(2))=0, Im(z_(1)z_(2))=0 then

Let z_(1)" and "z_(2) be two complex numbers such that z_(1)z_(2)" and "z_(1)+z_(2) are real then

If z_1a n dz_2 are two nonzero complex numbers such that = |z_1+z_2|=|z_1|+|z_2|, then a rgz_1-a r g z_2 is equal to -pi b. pi/2 c. 0 d. pi/2 e. pi

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