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Mathematics
Problem
Consider three complex numbers
z
1
z_{1}
z
1
,
z
2
z_{2}
z
2
, and
z
3
z_{3}
z
3
representing the vertices of a triangle.
z
1
=
2
+
2
i
z_{1} = 2 + 2i
z
1
=
2
+
2
i
and
z
2
=
2
−
2
i
z_{2} = 2 - 2i
z
2
=
2
−
2
i
are fixed. If
z
3
z_{3}
z
3
satisfies
∣
z
3
∣
=
6
|z_{3}| = 6
∣
z
3
∣
=
6
, find the Cartesian equation of the locus of the centroid
z
z
z
of the triangle.
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