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

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

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

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

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: if z_1 = 3 + 2i and z_2 = 5 - 4i , then |z_1 + z_2| is