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in Complex Numbers by (48.8k points)
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State True of False:

The inequality |z – 4| < |z – 2| represents the region given by x > 3.

1 Answer

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Best answer

True

Explanation:

Given |z – 4| < |z – 2|

Putting z = x + iy,

⇒ |x – 4 + iy| < |x – 2 + iy|

⇒ (x – 4)2 + y2 < (x – 2)2 + y2

⇒ x2 – 8x + 16 + y2 < x2 – 4x + 4 + y2

⇒ -8x + 16 < -4x + 4

⇒ 4x > 12

∴ x > 3

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