Let `|(( bar z _1)-2( bar z _2))//(2-z_1( bar z _2))|=1` and `|z_2|!=1`,where `z_1` and `z_2` are complex numbers. Show that `|z_1|=2.`

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

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)=3-4i , z_(2)=2+i find bar(z_(1)z_(2))

If |z_(1)+ z_(2)|=|z_(1)|+|z_(2)| , then arg z_(1) - arg z_(2) is

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

If z is non zero complex number, such that 2i z^(2) = bar(z), then |z| is

Let A(z_1) and (z_2) represent two complex numbers on the complex plane. Suppose the complex slope of the line joining A and B is defined as (z_1-z_2)/(bar z_1-bar z_2) .If the line l_1 , with complex slope omega_1, and l_2 , with complex slope omeg_2 , on the complex plane are perpendicular then prove that omega_1+omega_2=0 .

If z_1 + z_2 + z_3 + z_4 = 0 where b_1 in R such that the sum of no two values being zero and b_1 z_1+b_2z_2 +b_3z_3 + b_4z_4 = 0 where z_1,z_2,z_3,z_4 are arbitrary complex numbers such that no three of them are collinear, prove that the four complex numbers would be concyclic if |b_1b_2||z_1-z_2|^2=|b_3b_4||z_3-z_4|^2 .

Find the radius and centre of the circle z bar(z) - (2 + 3i)z - (2 - 3i)bar(z) + 9 = 0 where z is a complex number