" 3.If "|z_(1)k1" and "|(z_(1)-z_(2))/(1-bar(z)_(1)z_(2))|<1" then prove that "|z_(2)|<1

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

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

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

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)

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)

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)

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)

For two unimodular complex numbers Z_(1) and Z_(2), [(bar(z_(1)),-z_(2)),(bar(z_(2)),z_(1))]^(-1)[(z_(1),z_(2)),(-bar(z_(2)),bar(z_(1)))]^(-1) is equal to a) [(z_(1),z_(2)),(bar(z)_(1),bar(z)_(2))] b) [(1,0),(0,1)] c) [(1//2,0),(0,1//2)] d)None of these

Let z_(1), z_(2) be two non-zero complex numbers such that |z_(1) + z_(2)| = |z_(1) - z_(2)| , then (z_(1))/(bar(z)_(1)) + (z_(2))/(bar(z)_(2)) equals

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))