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Question Number 21308 by Tinkutara last updated on 20/Sep/17
Find all complex numbers z such that  ∣z − ∣z + 1∣∣ = ∣z + ∣z − 1∣∣
$$\mathrm{Find}\:\mathrm{all}\:\mathrm{complex}\:\mathrm{numbers}\:{z}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid{z}\:−\:\mid{z}\:+\:\mathrm{1}\mid\mid\:=\:\mid{z}\:+\:\mid{z}\:−\:\mathrm{1}\mid\mid \\ $$

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