It may be
Since it is mental arithmetic and no restrictions.
$3, -3, 4i, -4i$
since:
a) $3 -3 =0$
b) $3 + 4i = (2 + i)(2 + i)$
c) $3 - 4i = (2 - i)(2 - i)$
d) $-3 + 4i = (1 + 2i)(1 + 2i)$
e) $-3 - 4i = (1 - 2i)(1 - 2i)$
f) $4i - 4i = 0$
and also:
$3 - 3 + 4i - 4i =0$
