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AMC 12/AHSME
1984 AMC 12/AHSME
10
Fourth complex number
Fourth complex number
Source:
October 15, 2005
complex numbers
Problem Statement
Four complex numbers lie at the vertices of a square in the complex plane. Three of the numbers are
1
+
2
i
,
−
2
+
i
1+2i,-2+i
1
+
2
i
,
−
2
+
i
and
−
1
−
2
i
-1-2i
−
1
−
2
i
. The fourth number is A.
2
+
i
2+i
2
+
i
B.
2
−
i
2-i
2
−
i
C.
1
−
2
i
1-2i
1
−
2
i
D.
−
1
+
2
i
-1+2i
−
1
+
2
i
E.
−
2
−
i
-2-i
−
2
−
i
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