Show that for $z $ a complex number, there exists a complex number $\alpha $, wiht $|\alpha |=1$ such that $\alpha z = |z |$

Question

How can I show that for $z $ a complex number, there exists a complex number $\alpha $, wiht $|\alpha |=1$ such that $\alpha z = |z |$

Thanks in advance!

Answer 1

The answer is $\;\alpha={\overline z\over |z|}$ (the conjugate of z divided by $|z|$).

Can you see why?