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2014 District Olympiad
1
A complex equation
A complex equation
Source: Romanian District Olympiad 2014, Grade 10, P1
June 15, 2014
conics
ellipse
complex numbers
algebra proposed
algebra
Problem Statement
Solve for
z
∈
C
z\in \mathbb{C}
z
∈
C
the equation :
∣
z
−
∣
z
+
1
∣
∣
=
∣
z
+
∣
z
−
1
∣
∣
|z-|z+1||=|z+|z-1||
∣
z
−
∣
z
+
1∣∣
=
∣
z
+
∣
z
−
1∣∣
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