locus of z, where z=u-i/u-2 (1 Viewer)

[member 6003]

a) If u is purely real
b) If u moves around a unit circle

no idea for both of them, a hint would be appreciated

 

[okkk]

If the equation is in terms of z, it's hard to apply the conditions, so re-arrange in terms of u. This gives us u=(2z-i)/(z-1). Then if u is purely real, you know that Im[(2z-i)/(z-1)]=0, which you can find the locus of by letting z=x+iy. Similarly, if u moves around the unit circle, you know that |(2z-i)/(z-1)|=1, which you can then find the locus of using z=x+iy.

 

[member 6003]

thanks