Question 30
Given that $w$ and $z$ are complex numbers such that $|w+z|=1$ and $|w^{2}+z^{2}|=14$, find the smallest possible value of $|w^{3}+z^{3}|$. Here, $|\cdot|$ denotes the absolute value of a complex number, given by $|a+b i|=\sqrt{a^{2}+b^{2}}$ whenever $a$ and $b$ are real numbers.