If `|z_(1)|=|z_(2)|, "is it necesssary that "z_(1) = z_(2)`.

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

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

If |z_(1)|=|z_(2)|=......=|z_(n)|=1, prove that |z_(1)+z_(2)+z_(3)++z_(n)|=(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))++(1)/(z_(n))

if |z_(1)+z_(2)|=|z_(1)|+|z_(2)|, then prove that arg(z_(1))=arg(z_(2)) if |z_(1)-z_(2)|=|z_(1)|+|z_(2)| then prove that arg (z_(1))=arg(z_(2))=pi

If |z_(1)| = |z_(2)| = 1, z_(1)z_(2) ne -1 and z = (z_(1) + z_(2))/(1+z_(1)z_(2)) then

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

If |z_(1)|=1,|z_(2)|=2, then value of |z_(1)+z_(2)|^(2)+|z_(1)-z^(2)|^(2) is equal to

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