Math miscellaneousEasy
Question
If |z-4| < |z-2|, its solution is given by
Options
A.Re(z) > 0
B.Re(z) < 0
C.Re (z) > 3
D.Re(z) > 2
Solution
Given | z - 4 | < | z - 2 | Let z = x + iy
⇒ |(x-4) + iy)| < |(x-2) + iy| ⇒ (x -4)2 + y2 < (x - 2)2 + y2
⇒ x2 - 8x + 16 < x2 - 4x + 4 ⇒ 12 < 4 x ⇒ x > 3 ⇒ Re(z) > 3
⇒ |(x-4) + iy)| < |(x-2) + iy| ⇒ (x -4)2 + y2 < (x - 2)2 + y2
⇒ x2 - 8x + 16 < x2 - 4x + 4 ⇒ 12 < 4 x ⇒ x > 3 ⇒ Re(z) > 3
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