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Mathematics
Mathematics
Problem
Let
z
1
z_1
z
1
and
z
2
z_2
z
2
be two complex numbers such that
∣
z
2
∣
=
1
|z_2| = 1
∣
z
2
∣
=
1
and
z
1
−
1
z
1
+
1
=
(
z
2
−
1
z
2
+
1
)
2
\frac{z_1 - 1}{z_1 + 1} = \left( \frac{z_2 - 1}{z_2 + 1} \right)^2
z
1
+
1
z
1
−
1
=
(
z
2
+
1
z
2
−
1
)
2
, then the maximum value of
∣
z
1
−
1
∣
+
∣
z
1
+
1
∣
|z_1 - 1| + |z_1 + 1|
∣
z
1
−
1∣
+
∣
z
1
+
1∣
is - - - .
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