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Mathematics
Problem
If
z
1
,
z
2
z_1, z_2
z
1
,
z
2
and
z
3
z_3
z
3
are the vertices of an equilateral triangle with
z
0
z_0
z
0
as its circumcentre, then changing origin to
z
0
z_0
z
0
, show that
Z
1
2
+
Z
2
2
+
Z
3
2
=
0
Z_1^2 + Z_2^2 + Z_3^2 = 0
Z
1
2
+
Z
2
2
+
Z
3
2
=
0
, where
Z
1
,
Z
2
,
Z
3
Z_1, Z_2, Z_3
Z
1
,
Z
2
,
Z
3
are new complex numbers of the vertices.
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