Simple complex number problem (1 Viewer)

[Lola_teapot]

I am having trouble answering this simple complex number problem:

z / (z - i) is real. Show that z is imaginary

Some help would be really useful. Thanks

 

[ninetypercent]

Let z/(z-i )= a where a is real

therefore,

az - ai = z
-ai = z - az
-ai = z(1-a)
z = -ai/(1-a)

hence, z is imaginary