For z=2+3i, verify the following: (z+ `bar z`) is real

For z=2+3i, verify the following: (z- bar z ) = 6i

For z=2+3i, verify the following: bar bar z = z

For z=2+3i, verify the following: z bar z = abs(z)^2

z_1 = 1+i, z_2 =2-3i, verify the following: bar (z_1+z_2) = bar (z_1) + bar (z_2)

z_1 = 1+i, z_2 =2-3i, verify the following: bar (z_1-z_2) = bar (z_1) - bar (z_2)

z_1 = 1+i, z_2 =2-3i, verify the following: bar (z_1. z_2) = bar (z_1) . bar (z_2)

z_1 = 1+i, z_2 =2-3i, verify the following: bar (z_1/ z_2) = bar (z_1) / bar (z_2)

z_1 = 1 + i, z_2 = 2 - 3i , verify the following. bar(z_1 . z_2) = bar z_1 . bar z_2

z_1 = 1 + i, z_2 = 2 - 3i , verify the following. bar(z_1 / z_2) = bar z_1 / bar z_2

Select and write the correct answer from the given alternatives in each of the following: z + bar z != 0 , if and only if