(1 point) If z is a complex number then say \ bar {z} = \ text {Re} (z) - \ text {Im} (z) i be its conjugate and | z | = \ sqrt {\ text { Re} (z) ^ 2 + \ text {Im} (z) ^ 2} its absolute amount (or distance to the origin in the complex number plane). Also let \ bar {\ bar {z}} denote the conjugate of \ bar {z}. With this in mind, decide which of the following statements are true.

A. The ratio of two zero-complex numbers is a complex number.

B. i ^ n = i if n \ equiv_4 1.

C. If \ text {Re} (z) is a rational number, then \ bar {\ bar {z}} + \ bar {z} is a rational number.

D. \ text {Im} (z \ cdot \ bar {z}) = 0 for complex numbers z.

E. (z-z_0) (z- \ bar {z} _0) = z ^ 2-2 \ text {Re} (z_0) z + | z_0 | ^ 2 for all complex numbers z and z_0.