Synolakis [1] has proved that the equation
\[
J
0
(
z
)
−
i
J
1
(
z
)
=
0
{J_0}\left ( z \right ) - i{J_1}\left ( z \right ) = 0
\]
has no zeros in the half plane Im
z
>
0
z > 0
. In this note a table of the first thirty roots, correct to
O
(
10
−
6
)
O\left ( {{{10}^{ - 6}}} \right )
, is presented and an asymptotic formula, which is correct to better than one tenth of one percent for the smallest zero, is derived.