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Mathematics
Mathematics
Problem
Let
S
S
S
be the set of all complex numbers
z
z
z
satisfying
z
4
−
∣
z
∣
4
=
4
i
z
2
z^4 - |z|^4 = 4iz^2
z
4
−
∣
z
∣
4
=
4
i
z
2
. Then, the minimum possible value of
∣
z
1
−
z
2
∣
2
|z_1 - z_2|^2
∣
z
1
−
z
2
∣
2
, where
z
1
,
z
2
∈
S
z_1, z_2 \in S
z
1
,
z
2
∈
S
, with
Re
(
z
1
)
>
0
\operatorname{Re}(z_1) > 0
Re
(
z
1
)
>
0
and
Re
(
z
2
)
<
0
\operatorname{Re}(z_2) < 0
Re
(
z
2
)
<
0
, is — — — —.
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