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Distance Formula

Find locus of...

Question

Find locus of z if Re(1/z)<1/2

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Solution

Z = x + i y
Re(1/z) = x/(x^2+y^2) = 1/2
so 1/2x^2 - x + 1/2 y ^2 = 0
(x - 1/4)^2 + y^2 = 1/ 16

This is a circle with radius 1/4 and center (1/4, 0).

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