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Mathematics
Problem
The points
z
1
z_1
z
1
,
z
2
z_2
z
2
,
z
3
z_3
z
3
and
z
4
z_4
z
4
in the complex plane are the vertices of a parallelogram taken in order, if and only if (a)
z
1
+
z
4
=
z
2
+
z
3
z_1 + z_4 = z_2 + z_3
z
1
+
z
4
=
z
2
+
z
3
(c)
z
1
+
z
2
=
z
3
+
z
4
z_1 + z_2 = z_3 + z_4
z
1
+
z
2
=
z
3
+
z
4
(b)
z
1
+
z
3
=
z
2
+
z
4
z_1 + z_3 = z_2 + z_4
z
1
+
z
3
=
z
2
+
z
4
(d) None of these
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