SOLUTION: Please help me solve this:
If z is a complex number such that the real part of (z+1)/(z-i) is 1, show that z lies on a straight line.
I tried to to multiply by the conjugate of
Question 981343: Please help me solve this:
If z is a complex number such that the real part of (z+1)/(z-i) is 1, show that z lies on a straight line.
I tried to to multiply by the conjugate of the denominator and expanded and simplified and separated the the real and imaginary parts and got
{{x^2+y^2-y+x+i{x-y+1}}/{x^2+y^2-2y+1}
than I dropped the imaginary part i{x-y+1} and let the real part equal 1
{x^2+y^2-y+x}/{x^2+y^2-2y+1}=1
{x^2+y^2-y+x}=1{x^2+y^2-2y+1}
so I got y=1-x
Is that correct or have I missed anything?
Thank you very much, Jenny
