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Mathematics
Mathematics
Problem
If the complex number
z
z
z
satisfying
(
z
−
z
ˉ
)
2
=
12
∣
z
∣
2
−
4
(z - \bar{z})^2 = 12|z|^2 - 4
(
z
−
z
ˉ
)
2
=
12∣
z
∣
2
−
4
, then find the maximum value of
3
3
Re
(
z
)
+
8
Im
(
z
)
3\sqrt{3} \operatorname{Re}(z) + 8 \operatorname{Im}(z)
3
3
Re
(
z
)
+
8
Im
(
z
)
.
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