" If "|z_(1)+z_(2)|>|z_(1)-z_(2)|" then prove that "-(pi)/(2)

If |z_(1)+z_(2)|>|z_(1)-z_(2) then prove that -(pi)/(2)

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)and z_(2) be any two non-zero complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then prove that, arg z_(1)=arg z_(2) .

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

If z_(1) , z_(2) are complex numbers and if |z_(1) + z_(2)| = |z_(1) - z_(2)| show that are (z_(1)) - arg (z_(2)) = pm (pi)/(2)

Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=1 then prove that |z_(1)+z_(2)+z_(3)|=|z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)|

If z_(1) , z_(2) are complex numbers and if |z_(1) + z_(2)| = |z_(1)| - |z_(2)| show that arg (z_(1)) - arg (z_(2)) = pi .

if |z_1+z_2|=|z_1|+|z_2|, then prove that a r g(z_1)=a r g(z_2) if |z_1-z_2|=|z_1|+|z_2|, then prove that a r g(z_1)=a r g(z_2)=pi

If z_(1)&z_(2) are two complex numbers & if arg (z_(1)+z_(2))/(z_(1)-z_(2))=(pi)/(2) but |z_(1)+z_(2)|!=|z_(1)-z_(2)| then the figure formed by the points represented by 0,z_(1),z_(2)&z_(1)+z_(2) is:

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