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The set of points z in the complex plane satisfying |z - 4| < |z - 2| corresponds to which region?

1. Re(z) > 0
2. Re(z) < 0
3. Re(z) > 3
4. none

Correct answer: Re(z) > 3

Solution

Points nearer to 4 than to 2 lie to the right of the bisector x = 3, i.e. Re(z) > 3.

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