Exercise 833Algebra › Complex numbersL1Added 3 Nov 2026

A locus defined by a modulus equation

#locus#modulus#geometric interpretation

Statement

Describe the set of points $M$ with affix $z$ such that $|z-1|=2$ .

Hint

$|z-1|=2$ means the distance from $M$ to the point of affix $1$ is $2$ .

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Interpretation. $|z-1|$ is the distance between the point of affix $z$ and the point of affix $1$ .

Locus. The set of points at distance $2$ from the point $1$ is the circle of center $1$ and radius $2$ .

Conclusion. The locus is the circle with center $A(1,0)$ and radius $2$ .