The discussion centers on the properties of the absolute value function, specifically addressing the incorrect assumption that abs(a + b) equals abs(a) + abs(b) for complex numbers. The correct formulation for the absolute value of a complex number z = x + iy is abs(z) = √[x² + y²], which contradicts the erroneous claim that abs(z) can be expressed as abs(x) + i abs(y). The participants emphasize that the initial hypothesis is flawed, rendering subsequent conclusions invalid.
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Jhenrique said:If the abs(a+b) = abs(a) + abs(b), so the abs(z) = abs(x+iy) = abs(x) + abs(iy) = abs(x) + i abs(y). However, the correct wouldn't be abs(z) = √[x²+y²] ?
√[x²+y²] ≠ abs(x) + i abs(y) => abs(z) ≠ abs(z)
It's no make sense. What there is of wrong with those definions?
As PeroK notes, this is incorrect. Since your hypothesis is false, any following work is meaningless.Jhenrique said:If the abs(a+b) = abs(a) + abs(b)
Jhenrique said:, so the abs(z) = abs(x+iy) = abs(x) + abs(iy) = abs(x) + i abs(y). However, the correct wouldn't be abs(z) = √[x²+y²] ?
√[x²+y²] ≠ abs(x) + i abs(y) => abs(z) ≠ abs(z)
It's no make sense. What there is of wrong with those definions?