If`z_(1),z_(2)inC,z_(1)^(2)+z_(2)^(2)inR,z_(1)(z_(1)^(2)-3z_(2)^(2))=2` and `z_(2)(3z_(1)^(2)-z_(2)^(2))=11,` the value of `z_(1)^(2)+z_(2)^(2)` is

If z=(1+i)/(√2) , then the value of z^(1929) is

If z^(1) =2 -I, z_(2)=1+i , find |(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)|

If |z_(1)|=2,|z_(2)|=3,|z_(3)|=4and|z_(1)+z_(2)+z_(3)|=5. then |4z_(2)z_(3)+9z_(3)z_(1)+16z_(1)z_(2)| is

If z_(1),z_(2),z_(3) andz_(4) are the roots of the equation z^(4)=1, the value of sum_(i=1)^(4)(z_i)^(3) is

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

If |z_(1)|=|z_(2)|andamp(z_(1))+amp(z_(2))=0, then

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

Let z_(1),z_(2) and z_(3) be three non-zero complex numbers and z_(1) ne z_(2) . If |{:(abs(z_(1)),abs(z_(2)),abs(z_(3))),(abs(z_(2)),abs(z_(3)),abs(z_(1))),(abs(z_(3)),abs(z_(1)),abs(z_(2))):}|=0 , prove that (i) z_(1),z_(2),z_(3) lie on a circle with the centre at origin. (ii) arg(z_(3)/z_(2))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))^(2) .

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

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