A circle given by a modulus equation

#modulus#circle#locus

Statement

Describe the set of $z$ such that $|z-1+i|=3$ .

Hint

$|z-(1-i)|=3$ is a circle.

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Rewrite. $|z-(1-i)|=3$ .

Interpretation. The distance from $z$ to the point of affix $1-i$ equals $3$ .

Conclusion. The locus is the circle with center $A(1,-1)$ and radius $3$ .