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