16

Part of 2017 Harvard-MIT Mathematics Tournament

Problems(1)

2017 Guts #16: Complex nonlinear system

Source:

a

b

be complex numbers satisfying the two equations \begin{align*} a^3 - 3ab^2 & = 36 \\ b^3 - 3ba^2 & = 28i. \end{align*} Let

M

be the maximum possible magnitude of

a

a

|a| = M

algebracomplex numbers