Does 1/z = z(bar) (1 Viewer)

[spyris]

Hi, I heard somewhere that 1/z = z(bar) but im not sure if its true because i am unable to prove it...so is it true and if so how do i show it. THanks

 

[HSC2014]

It does not You can quickly obtain the complex number that is 1/z where z = x + iy by rationalising the denominator and you'll see it comes out NOT to be z|

 

[funnytomato]

in general, no

but if |z|= 1
then z= cis theta, and
1/z= cis 0 / cis theta = cis (-theta)= z bar

 

[braintic]

Adding to funnytomato's comment, it is useful result in some questions concerning roots of UNITY. But ONLY unity.

A more general result is 1/z = (z bar) / |z|