  It is shown that the real part of the complementary error function is bounded
below by 1 in the subset of the complex plane where the principal argument is
between $3\pi/4$ and $5\pi/4$. This improves a previous result asserting that
the complementary error function has no zeros in the same set, whose proof was
essentially based on calculus of two variables. The present proof uses an
almost $60$ years old, relatively unknown estimate for the error function,
combined with some elementary complex analysis, thus serving as a humble
illustration to a quote attributed to Jacques Hadamard: "The shortest path
between two truths in the real domain passes through the complex domain".
