For all z C, prove that (i) (ii) . (iii) = |z| 2 (iv) is real (v) is 0 or imaginary.

Question

Philoid · Accepted Answer

Let z = a + ib

Hence Proved.

(ii) Let z = a + ib

Hence, Proved.

(iii) Let z = a + ib

Hence Proved.

(iv) Let z = a + ib

Hence , is real.

(v) Case 1. Let z = a + 0i

Case 2. Let z = 0 + bi

Case 2. Let z = a + ib

Thus, is 0 or imaginary.