" 20.If "|(z_(1)-z_(2))/(1-bar(z)_(1)z_(2))|<1," then "z_(1),z_(2)" both lie inside or both lie out side the circle "|z|=R" ,then find value of "R

If |z_(1)|!=1,|(z_(1)-z_(2))/(1-bar(z)_(1)z_(2))|=1, then

If z_(1) and z_(2) two different complex numbers and |z_(2)|=1 then prove that |(z_(2)-z_(1))/(1-bar(z)_(1)z_(2))|=1

if z_(1) and z_(2) are 1-i,-2+4i respectively find Im((z_(1)z_(2))/(bar(z)_(1)))

If (4z_(1))/(9z_(2))+(4bar(z_(1)))/(9bar(z_(2)))=0, then the value of |(z_(1)-z_(2))/(z_(1)+z_(2))| is

Let Z_(1) and z_(2) be two complex numbers with z_(1)!=z_(2) if |z_(1)|=sqrt(2), then |(z_(1)-bar(z)_(2))/(2-z_(1)z_(2))| equals

Let z_(1) and z_(2) be two complex numbers such that |(z_(1)-2z_(2))/(2-z_(1)bar(z)_(2))|=1 and |z_(2)|!=1, find |z_(1)|

If z_(1) and z_(2) are two complex numbers,then (A) 2(|z|^(2)+|z_(2)|^(2)) = |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2) (B) |z_(1)+sqrt(z_(1)^(2)-z_(2)^(2))|+|z_(1)-sqrt(z_(1)^(2)-z_(2)^(2))| = |z_(1)+z_(2)|+|z_(1)-z_(2)| (C) |(z_(1)+z_(2))/(2)+sqrt(z_(1)z_(2))|+|(z_(1)+z_(2))/(2)-sqrt(z_(1)z_(2))|=|z_(1)|+|z_(2)| (D) |z_(1)+z_(2)|^(2)-|z_(1)-z_(2)|^(2) = 2(z_(1)bar(z)_(2)+bar(z)_(1)z_(2))

If z_(1),z_(2) are complex numbers such that |(z_(1)-3z_(2))/(3-z_(1)bar(z)_(2))|=1 and |z_(2)|!=1 then find |z_(1)|

For two unimobular complex numbers z_(1) and z_(2) , find [(bar(z)_(1),-z_(2)),(bar(z)_(2),z_(1))]^(-1) [(z_(1),z_(2)),(-bar(z)_(2),bar(z)_(1))]^(-1)