Mathematics · Complex Numbers

For any two complex numbers z1 and z2, which of the following statements is always true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1|z1| + |z2| < |z1 + z2|
2|z1 + z2|2 + |z1 - z2|2 = 2(|z1|2 + |z2|2)✓
3|z1 - z2|2 > |z1|2 + |z2|2 - 2Re(z1·z̄2)
4|z1 + z2|2 < |z1|2 + |z2|2 + 2Re(z1·z̄2)

Correct answer

|z1 + z2|2 + |z1 - z2|2 = 2(|z1|2 + |z2|2)

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For any two complex numbers z1 and z2, which of the following statements is always true?

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For any two complex numbers z1 and z2, which of the following statements is always true?

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