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

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

If z^2 = -24-18i , then z=

Select and write the correct answer from the given alternatives in each of the following: If (1 + i) z = 1 (1 - i) bar z , then z is

If z_1 and z_2 are two non-zero complex numbers such that abs(z_1+z_2) = abs(z_1)+abs(z_2) , then arg(z_1)-arg(z_2) is equal to

If z_1 = (4,5) and z_2 = (-3,2) , then frac{z_1}{z_2} equals

If z_1 = 1-i and z_2 = 2+4i , then im[frac{z_1z_2}{z_1} =