Complex Analysis: Theory and Applications · Problem 4.2.7

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · mandelbrot-set-symmetry

Problem

Prove that if a complex number

c

is in the Mandelbrot set, then its conjugate

\bar{c}

is also in the Mandelbrot set. Thus, the Mandelbrot set is symmetric about the

x

axis. Hint: Use mathematical induction.