(a) Let the function f be defined on the complex numbers as \(f(z) = (1+i)z.\) Prove that the distance between f(z) and 0 is a constant multiple of the distance between f(z) and z, and find the value of this constant.

(b) Let the function g be defined on the complex numbers as \(g(z) = (a + 2 i)z\) for some real value of a. Then if g(z) is equidistant from 0 and z for all z, what is a equal to?

Guest Dec 5, 2019