In this brief note, we study algebraic elements in the complex group algebra
C
[
G
]
{\mathbf {C}}[G]
. Specifically, suppose
ξ
∈
C
[
G
]
\xi \in {\mathbf {C}}[G]
satisfies
f
(
ξ
)
=
0
f(\xi ) = 0
for some nonzero polynomial
f
(
x
)
∈
C
[
x
]
f(x) \in {\mathbf {C}}[x]
. Then we show that a certain fairly natural function of the coefficients of
ξ
\xi
is bounded in terms of the complex roots of
f
(
x
)
f(x)
. For
G
G
finite, this is a recent observation of [HLP]. Thus the main thrust here concerns infinite groups, where the inequality generalizes results of [K] and [W] on traces of idempotents.