  Ball's complex plank theorem states that if $v_1,\dots,v_n$ are unit vectors
in $\mathbb{C}^d$, and $t_1,\dots,t_n$, non-negative numbers satisfying
$\sum_{k=1}^nt_k^2 = 1,$ then there exists a unit vector $v$ in $\mathbb{C}^d$
for which $|\langle v_k,v \rangle | \geq t_k$ for every $k$. Here we present a
streamlined version of Ball's original proof.
