For any two complex numbers, `z_1` and `z_2`, prove that Re(`z_1` `z_2`) = [(Re(`z_1`). Re(`z_2`)] - [Im(`z_1`). Im(`z_2`)]

For any two complex numbers z_1 and z_2 and any real numbers a and b, [abs(az_1-bz_2)]^2+[abs(bz_1+az_2)]^2 =

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

Let z_1 and z_2 be two complex numbers such that z_1+z_2 and z_1z_2 both are real, theb

if for the complex numbers z_1 and z_2 abs(1-barz_1z_2)^2-abs(z_1-z_2)^2 = k(1-abs(z_1)^2)(1-abs(z_2)^2) , then k is equal to

For any non zero complex number z, the minimum value of abs(z)+abs(z-1) is

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)

If abs(z_1) = abs(z_2) , is it necessary that z_1 = z_2 ?

If z_1 and z_2 are any complex numbers, then abs(z_1+z_2)^2+abs(z_1-z_2)^2 is equal to

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