(complexe numbers) Show that? Thank you!

Is z ∈ C \ {0}, than is $| z \frac{|}{z}$ a square root of ${z}^{-} / z$

Jan 15, 2018

yes

Explanation:

multiply and divide $R H S$ by $z$
so we get
$z {z}^{-} / {\left(z\right)}^{2}$ = $| z {|}^{2} / {\left(z\right)}^{2}$ = ${\left(| z \frac{|}{z}\right)}^{2}$
hence
$| z \frac{|}{z}$ will be a square root of the ${z}^{-} / z$ which is ${\left(L H S\right)}^{2}$
hope u find it helpful :)