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Is this true? |z1+z2|^2 = (z1+z2)^2, zEC?
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- PopeLv 78 months agoFavorite Answer
I do not get the zEC part, but I think I get the rest of it.
The expression |z₁ + z₂|² is real in all cases, but (z₁ + z₂)² is not necessarily real at all. Consider this counterexample:
z₁ = -1
z₂ = i
|z₁ + z₂|²
|-1 + i|²
= √[1² + (-1)²]²
= √(2)²
= 2
(z₁ + z₂)²
= (-1 + i)²
= (-1)² + i² - 2i
= 1 - 1 - 2i
= -2i
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