How to sketch a line from complex numbers

[polaris90]

sketch the line described by the equation |z - u| = |z|
u = -1 + j√3

I don't understand how to do this. I'm not sure of what z is exactly. Can anybody explain to me what it is?

 

[SammyS]

sketch the line described by the equation |z - u| = |z|
u = -1 + j√3

I don't understand how to do this. I'm not sure of what z is exactly. Can anybody explain to me what it is?

z is a general complex number. It's often represented if the xy-plane (the Argand plane) by letting x be the real part of z and letting y be the imaginary part of z, i.e. z = x + jy, where x & y are real variables.

So, solve |x + jy -(-1 + j√3)| = |x + jy| for y in terms of x, or x in terms of y.