Q. 26 F5.0( 3 Votes )

State True of False for the following:

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

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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