Complex Numbers

If |z - 4| < |z - 2|, its solution is given by

  1. Re(z) > 3
  2. Re(z) > 0
  3. Re(z) < 0
  4. Re(z) > 2

Solution

|z – 4| < |z – 2|

By taking, z = a + ib

|(a – 4) + ib| < |(a – 2) + ib|

(a – 4)2 + b2 < (a – 2)2 + b2

a2 + 16 - 8a < a2 + 4 - 4a

-8a + 4a < -16 + 4

- 4a < -12

4a > 12

a > 3

The correct option is A.