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Teaching myself Linear Algebra and got stuck on the following question for complex numbers:
Show that $|z| \geq 0$ and $|z|=0$ if and only if $z=0.$
Now, the question itself seems pretty obvious where $z=x+iy$ and $|z|=\sqrt{x^2+y^2}$ but I am a bit confused regarding how to tie everything together. Thanks in advance.

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1 Answer

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Now, $|Z|= 0$ implies that $\sqrt{x^2+y^2}=0$ which implies that $x^2+y^2=0$. Under what circumstances will the last equality hold?

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