Complex Analysis: Theory and Applications · Problem 5.3.5

Elementary Functions — Howell & Matthews

Mathematics — Complex Analysis · complex-exponents-difference-equation

Problem

Let

z_n = (1+i)^n

for

n = 1, 2, \ldots

. Show that the sequence

\{z_n\}

is a solution to the difference equation

z_n = 2z_{n-1} - 2z_{n-2}

for

n \geq 3