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Prove that, if \( z_{1} \) and \( z_{2} \) are two complex numbers and \( c0 \), then \( \left|z_{1}+z_{2}\right|^{2} \leq(1+c)\left|z_{1}\right|^{2}+\left(1+\frac{1}{c}\right)\left|z_{2}\right|^{2} \).
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