Prove all the claims of Proposition 9.5, for 2 = x+yi, w = a + bi C: (f) 2 = 2/|2| for z #0 (g) |z| = 0 iff z=0 (h) || = |2| (i) |zw| = |z||w| (i) z + w||z|+|w| (a) z+w=2+ w (b) zw = z w (c) = z (d) z + z = 2x (e) z-z = 2yi Proposition 9.5. Let z = x+iy, w = a +ib E C. Then the conjugate satisfies: 3. Z = z 1. z+w=Z+w 2. zw z W And the absolute value satisfies: 1. |z| = 0 iff z = 0 2. |z| = |2| 4. 2+ z = 2x 5. z-z = 2yi 6. z 2/22 for z 0 3. |zw|=|z||w| 4. z+w||z|+|w|