If |`z_(1)`| = 1, `|z_(2)| = 2, |z_(3)| = 3 and |9z_(1)z_(2) + 4z_(1) z_(3) + z_(2) `
`z_(3) = 12|,` then the value of `|z_(1) + z_(2) + z_(3)|` is

If z_(1) = 1 - 3i, z_(2) = -4i and z_(3) = 5, show that (z_(1)z_(2)) z_(3) = z_(1) (z_(2)z_(3))

If z_(1) = 3, z_(2) = -7i, and z_(3) = 5 + 4i, show that (z_(1) + z_(2)) z_(3) = z_(1) z_(3) + z_(2) z_(3)

If z_(1) = 3, z_(2) = -7i, and z_(3) = 5 + 4i, show that z_(1)(z_(2) + z_(3)) = z_(1) z_(2) + z_(1) z_(3)

If z_(1),z_(2), and z_(3) are three complex numbers such that |z_(1)| = 1, " " |z_(2)| = 2, " " |z_(3)| = 3 and |z_(1) + z_(2) + z_(3) | = 1, show that |9z_(1)z_(2) + 4 z_(1)z_(3) + z_(2)z_(3)| = 6 .

If z_(1) = 1 - 3i, z_(2) = -4i and z_(3) = 5, show that (z_(1) + z_(2)) + z_(3) = z_(1) + (z_(2) + z_(3))

If z_(1),z_(2)andz_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=|z_(1)+z_(2)+z_(3)|=1 , find the value of |1/z_(1)+1/z_(2)+1/z_(3)| .

If z_(1)=4+3i , z_(2)=12-5i , z_(3)=8+6i find |z_(1)|,|z_(2)|,|z_(3)|,|z_(1)+z_(2)| and |z_(3)-z_(2)|

If |z_(1)+ z_(2)|=|z_(1)|+|z_(2)| , then arg z_(1) - arg z_(2) is

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