Question 22
Let $(a_n)$ and $(b_n)$ be the sequences of real numbers such that $$
(2 + i)^n = a_n + b_n i
$$ for all integers $n \ge 0,$ where $i = \sqrt{-1}.$ What is $$
\sum_{n=0}^{\infty} \frac{a_n b_n}{7^n}?
$$
(2 + i)^n = a_n + b_n i
$$ for all integers $n \ge 0,$ where $i = \sqrt{-1}.$ What is $$
\sum_{n=0}^{\infty} \frac{a_n b_n}{7^n}?
$$