What can we conclude about the norm of a complex vector (dimension 2) when it's equal to 0? What does it mean? What can be said about their components x and y?
x=(5+2i,-2+5i)
Well,
||x||^2 = (5+2i)^2 + (-2+5i)^2
||x||^2 = (25 + 10i + 4i^2) + ( 4 -10i + 25i^2)
||x||^2 = (25+10i-4) + (4-10i-25) if we let (i^2 = -1)
||x||^2 = 25 + 10i -4 + 4 - 10i - 25
||x||^2 = 0
||x|| = 0
? Is there any mistake in my calculations? The initial components of x were not 0, yet the norm is zero.
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