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I was going over the complex numbers and I came across the following inequality in my notes: $|z_1 + z_2| \leq z_1 + z_2$.

Is this correct? Because it doesn't look that way to me. And if so, what is the correct version, and in what kinds of exercises would this property be useful?

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Inequalities between complex numbers are meaningless. You need to have inequalities between moduli of complex numbers. If you put modulus signs round the z's on the right, it would be a true statement. – Old John Nov 4 '12 at 16:24
up vote 1 down vote accepted

I think you might have meant $|z_1+z_2| \leq |z_1| + |z_2|$. You can only have comparisons ($\leq$, $\geq$ etc.) between real numbers.

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