Find the locus in the complex plane of points that satisfy

[applestrudle]

Homework Statement

find the locus in the complex plane that satisfies

z -c = p (1+it/1-it)

c is complex, p is real t is a real parameter

Homework Equations

The Attempt at a Solution

there is no answer in the textbook so i wanted to check my answer. I got a unit circle which is offset by c, so that c is in the centre of the circle.

please confirm!
Thanks :)

 

[BruceW]

are you sure it is a unit circle? remember 'p' is a real number there. Also, you should really put parentheses where they are needed. The equation should be written z-c = p (1+it)/(1-it) because this is unambiguous, however z-c = p(1+it/1-it) is very ambiguous and could mean a lot of different things.