# Let #z=a+ib#, where #a# and #b# are real. If #z/(z-i)# is real, show that #z# is imaginary or #0#. Help?

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Let #z=a+ib# , where #a# and #b# are real. If #z/(z-i)# is real, show that #z# is imaginary or #0# .

Thanks!

Let

Thanks!

##### 1 Answer

Dec 31, 2017

Here's one method...

#### Explanation:

Note that:

#z/(z-i) = ((z-i)+i)/(z-i) = 1+i/(z-i) = 1+1/(z/i-1)#

If this is real then so is

So if