If `z_(1) and z_(2)` are two complex quantities, show that,
`|z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2[|z_(1)|^(2)+|z_(2)|^(2)].`

If z_(1),z_(2) are two complex numbers , prove that , |z_(1)+z_(2)|le|z_(1)|+|z_(2)|

If z_(1)and z_(2) are conjugate complex number, then z_(1)+z_(2) will be

z_(1) and z_(2) are two non-zero complex numbers such that z_(1)^(2)+z_(1)z_(2)+z_(2)^(2)=0 . Prove that the ponts z_(1),z_(2) and the origin form an isosceles triangle in the complex plane.

If z_(1) , z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 and iz_(1)=Kz_(2) , where K in R , then the angle between z_(1)-z_(2) and z_(1)+z_(2) is

z_1 and z_2 be two complex no. then prove that abs(z_1+z_2)^2+abs(z_1-z_2)^2=2[abs(z_1)^2+abs(z_2)^2]

If z_(1)+z_(2) are two complex number and |(barz_(1)-2bar z_(2))/(2-z_(1)barz_(2))|=1, |z_(1)| ne , then show that |z_(1)|=2 .

Let z_(1) and z_(2) be any two non-zero complex numbers such that 3|z_(1)|=2|z_(2)|. "If "z=(3z_(1))/(2z_(2)) + (2z_(2))/(3z_(1)) , then

If z_1 and z_2 are two complex no. st abs(z_1+z_2) = abs(z_1)+abs(z_2) then

z_(1) and z_(2)( ne z_(1)) are two complex numbers such that |z_(1)|=|z_(2)| . Sho that the real part of (z_(1)+z_(2))/(z_(1)-z_(2)) is zero.

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) .