Question 41
Let $a$ and $b$ be complex numbers satisfying the two equations
$$
\begin{aligned}
a^{3}-3 a b^{2} & =36 \\
b^{3}-3 b a^{2} & =28 i
\end{aligned}
$$
Let $M$ be the maximum possible magnitude of $a$. Find all $a$ such that $|a|=M$.
$$
\begin{aligned}
a^{3}-3 a b^{2} & =36 \\
b^{3}-3 b a^{2} & =28 i
\end{aligned}
$$
Let $M$ be the maximum possible magnitude of $a$. Find all $a$ such that $|a|=M$.