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Mathematics
Problem
If
z
1
z_1
z
1
and
z
2
z_2
z
2
are two complex numbers and
C
>
0
C > 0
C
>
0
, then prove that
∣
z
1
+
z
2
∣
2
≤
(
1
+
C
)
∣
z
1
∣
2
+
(
1
+
C
−
1
)
∣
z
2
∣
2
|z_1 + z_2|^2 \le (1 + C)|z_1|^2 + (1 + C^{-1})|z_2|^2
∣
z
1
+
z
2
∣
2
≤
(
1
+
C
)
∣
z
1
∣
2
+
(
1
+
C
−
1
)
∣
z
2
∣
2
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