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Some texts appear to define the complex modulus as the magnitude, that is $\sqrt{x^2 + y^2}$ of any complex number $z = x + iy$. Other texts seem to define the modulus as the square of that number, in other words the magnitude squared, or the product of $z$ and conjugate $\bar{z}$.

Which one of $|z|, |z|^2$ is the complex modulus?

Let $z = 3 + 4i$. Is modulus $|z|$ equal to $5$ or $25$ ?

mcandre
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    The modulus is defined everywhere as $|z|$. I've never seen it defined as $|z|^2$. Which text? – Kaynex Dec 30 '16 at 23:08
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    The term norm is used in both these senses while modulus is synonymous to just one of them, so we shouldn't be dismissing this question if the OP is translating into English. – Rob Arthan Dec 30 '16 at 23:26

1 Answers1

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The modulus of $z = x+iy$ is defined to be $|z| = \sqrt{x^2+y^2}$. Thus in your case $x = 3,y = 4 \implies |z| = 5$.

DeepSea
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