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 = 4 - 7i , z_2 = 2 + 3i and z_3 = 1 + i show that z_1 + (z_2 + z_3) = (z_1 + z_2)+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 .

Given z_1 = 1 + i, z_2 = 4 - 3i and z_3 = 2 + 5i verify that. z_1(z_2 - z_3) = z_1z_2-z_1z_3

If z_(1)=4+5i and z_(2)=-3+2i that (z_(1))/(z_(2)) is :

For any two complex number z_(1) and z_(2) , such that |z_(1)| = |z_(2)| = 1 and z_(1) z_(2) ne -1 , then show that (z_(1) + z_(2))/(1 + z_(1)z_(2)) is real number.

If z_(1)=3-4i , z_(2)=2+i find bar(z_(1)z_(2))