Re: Complex numbers (for geometry proof)

Fons a écrit :
What would be a short and straightforward way to prove that

|z-z_1| / |z-z_2| = a

(in which z_1 and z_2 are complex and a is real and independent of z) implies the existence of a complex number z_0 and a real number R (also independent of z) so that

|z-z_0| = R

maybe without having to calculate z_0 and R?


Short and straightforward? i dont know. I would either write some equations (and note that the resuting relation between real and imaginary parts of z is that of a circkle), or use the geometrical interpretation, getting what is known as "Leibniz problem"
.

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