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 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 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

If z_(1), z_(2),z_(3) ,are three complex numbers, prove that z_(1).Im(barz_(2)z_(3))+z_(2).Im(barz_(3)z_(1))+z_(3)Im(bar z_(1)z_(2))=0 where Im(W) = imaginary part of W,where W is a complex number.

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),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|Z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 , then find |z_(1)+z_(2)+z_(3)| .

If z_(1) , z_(2) are complex numbers such that Re(z_(1))=|z_(1)-2| , Re(z_(2))=|z_(2)-2| and arg(z_(1)-z_(2))=pi//3 , then Im(z_(1)+z_(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 .

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

If z_(1)andz_(2) be two non-zero complex numbers such that (z_(1))/(z_(2))+(z_(2))/(z_(1))=1 , then the origin and the points represented by z_(1)andz_(2)

Let z_(1)andz_(2) be complex numbers such that z_(1)nez_(2)and|z_(1)|=|z_(2)| . If Re(z_(1))gt0andIm(z_(2))lt0 , then (z_(1)+z_(2))/(z_(1)-z_(2)) is