Hey guys, i would appreciate a bit of help with my homework at the moment, this is a three part question taken from my math textbook (year 12). The first part (a.) was simple enough, sketch the circle defined by $\displaystyle x^2 + (y - 1)^2 = 1$. This was relatively simple, just a circle with an origin of (0,1) and a radius of 1.

These next few questions however have gotten me a little confused. Any help at all would be appreciated. I am not so much interested in the solution as i am with the method as i have several questions to do which are similar to this, so thorough explanation would be greatly appreciated if someone could manage this for me.

The point P(x,y) representing the non-zero complex number $\displaystyle z = x+iy$, lies on the circle C defined by $\displaystyle x^2 + (y - 1)^2 = 1$. Express Mod Z in terms of theta, the argument of Z.

Next, show that whatever the position of P on the circle C, the point P representing Z lies on a certain line, and determine the equation of this data line.

Thanks guys,