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Question
State True or False for the following:
The inequality |z – 4| < |z – 2| represents the region given by x > 3.
Options
True
False
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Solution
This statement is True.
Explanation:
Given that: |z – 4| < |z – 2|
Let z = x + yi
⇒ |x + yi – 4| < |x + yi – 2|
⇒ |(x – 4) + yi| < |(x – 2) + yi|
⇒ `sqrt((x - 4)^2 + y^2) < sqrt((x - 2)^2 + y^2)`
⇒ (x – 4)2 + y2 < (x – 2)2 + y2
⇒ (x – 4)2 < (x – 2)2
⇒ x2 + 16 – 8x < x2 + 4 – 4x
⇒ –8x + 4x < –16 + 4
⇒ –4x < –12
⇒ x > 3
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