Question

The inequality z – 4<z – 2represents the region given by

• A. Re (z) > 0
• B. Re (z) < 0
• C. Re (z) > 2
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Sol. |z – 4| < |z – 2| ⇒ |z – 4|² < | z – 2|² ⇒ (z – 4) ($\bar{z}$– 4)

<(z – 2)($\bar{z}$– 2) ⇒ z$\bar{z}$– 4(z +$\bar{z}$) + 16 < z$\bar{z}$ – 2(z +$\bar{z}$) + 4

⇒ 2(z +$\bar{z}$) > 12 ⇒ 4 Re (z) > 12 ⇒ Re (z) > 3