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Exams
Joint Entrance Examination
Mathematics
Complex Numbers
Question 335
Question 335 of 455
Easy
MCQ
∣
z
1
+
z
2
∣
2
+
∣
z
1
−
z
2
∣
2
|z_1+z_2|^2+|z_1-z_2|^2
∣
z
1
+
z
2
∣
2
+
∣
z
1
−
z
2
∣
2
is equal to:
A
2
(
∣
z
1
∣
+
∣
z
2
∣
)
2(|z_1|+|z_2|)
2
(
∣
z
1
∣
+
∣
z
2
∣
)
B
2
(
∣
z
1
∣
2
+
∣
z
2
∣
2
)
2(|z_1|^2+|z_2|^2)
2
(
∣
z
1
∣
2
+
∣
z
2
∣
2
)
C
∣
z
1
∣
∣
z
2
∣
|z_1||z_2|
∣
z
1
∣∣
z
2
∣
D
∣
z
1
∣
2
+
∣
z
2
∣
2
|z_1|^2+|z_2|^2
∣
z
1
∣
2
+
∣
z
2
∣
2
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Official solution
\[|z_1+z_2|^2+|z_1-z_2|^2=(|z_1|^2+|z_2|^2+2\operatorname{Re}(z_1\bar z_2))+(|z_1|^2+|z_2|^2-2\operatorname{Re}(z_1\bar z_2))=2(|z_1|^2+|z_2|^2).\]
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