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Mathematics
Mathematics
Problem
Let
z
z
z
be a complex number with non-zero imaginary part. If
2
+
3
z
+
4
z
2
2
−
3
z
+
4
z
2
\frac{2 + 3z + 4z^2}{2 - 3z + 4z^2}
2
−
3
z
+
4
z
2
2
+
3
z
+
4
z
2
is a real number, then the value of
∣
z
∣
2
|z|^2
∣
z
∣
2
is \_\_\_\_\_\_\_\_.
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