The inequality |z-4| < |z-2|represents the region given by

Q: 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

Sol. |z – 4| < | z-2|

⇒ | z- 4|2 < | z – 2|2

⇒ ( z-4) (z -4) < ( z-2) (z -2)

⇒ z z– 4(z + z) +16 < z – 2( z + z) + 4

⇒ 2( z + z ) > 12

⇒ 4Re (z) > 12

⇒ Re (z) > 3

Hence (D) is the correct answer.