  A Diophantine $m$-tuple is a set of $m$ distinct integers such that the
product of any two distinct elements plus one is a perfect square. It was
recently proven that there is no Diophantine quintuple in positive integers. We
study the same problem in the rings of integers of imaginary quadratic fields.
By using a gap principle proven by Diophantine approximations, we show that
$m\leqslant 42$. Our proof is relatively simple compared to the proofs of the
similar results in positive integers.
