Someone could help to prove the following inequality of modulus of complex numbers:
If $a\in\mathbb{C}$ then $|a|\leq|a+z| \qquad \forall z\in\mathbb{C}$
Someone could help to prove the following inequality of modulus of complex numbers:
If $a\in\mathbb{C}$ then $|a|\leq|a+z| \qquad \forall z\in\mathbb{C}$
It will be hard to prove. Try $a=1, z=-1$ where it is false.
It isn't true.
$a=1+i,\;z=-1-i$
This is false(!) Try $a = 1$, $z$ any negative number in $[-2, 0]$.