2017 Guts #16: Complex nonlinear system
Source:
February 21, 2017
algebracomplex numbers
Problem Statement
Let and be complex numbers satisfying the two equations
\begin{align*}
a^3 - 3ab^2 & = 36 \\
b^3 - 3ba^2 & = 28i.
\end{align*}
Let be the maximum possible magnitude of . Find all such that .