Let `z_(1)z_(2)andz_(3)` be three complex
numbers and `a,b,cin R,` such that `a+b+c=0andaz_(1)+bz_(2)+cz_(3)=0` then show that `z_(1)z_(2)and z_(3)` are
collinear.

z_(1) and z_(2) are two complex number such that |z_(1)|=|z_(2)| and arg (z_(1))+arg(z_(2))=pi , then show that z_(1)=-barz_(2)

If iz^(3)+z^(2)-z+i=0 then show that |z|=1.

If |z_(1)|=|z_(2)| , is the necessary that z_(1)=z_(2)

If the complex numbers z_(1) and z_(2) arg (z_(1))- arg(z_(2))=0 then showt aht |z_(1)-z_(2)|=|z_(1)|-|z_(2)| .

z_(1)=3+I and z_(2)=-2+6i then find z_(1)z_(2)

Let z_(1),z_(2) " and " z_(3) be three complex numbers in AP. bb"Statement-1" Points representing z_(1),z_(2) " and " z_(3) are collinear bb"Statement-2" Three numbers a,b and c are in AP, if b-a=c-b

z_(1)=9+3i and z_(2)=-2-i then find z_(1)-z_(2)

For any two complex numbers z_(1) and z_(2) , prove that Re ( z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)

z_(1)=4+3i and z_(2)=-8+5i then find z_(1)+z_(2) .

Numbers of complex numbers z, such that abs(z)=1 and abs((z)/bar(z)+bar(z)/(z))=1 is