If \( z_{1}, z_{2} \in \mathbf{C} \), show that \( \left(z_{1}+z_{2...

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If \( z_{1}, z_{2} \in \mathbf{C} \), show that \( \left(z_{1}+z_{2}\right)^{2}=z_{1}^{2}+2 z_{1} z_{2}+z_{2}^{2} \).
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