Find all complex numbers Z satisfying the following conditions at the same time （1） 1＜（z+10/z)≤6 (2) The real part and imaginary part of Z are all integers The second problem is "the real part and imaginary part of Z are all integers, so we can find the complex Z satisfying the condition."

Find all complex numbers Z satisfying the following conditions at the same time （1） 1＜（z+10/z)≤6 (2) The real part and imaginary part of Z are all integers The second problem is "the real part and imaginary part of Z are all integers, so we can find the complex Z satisfying the condition."

From 1 ＜ (Z + 10 / z) ≤ 6, we know that Z + 10 / Z must be a real number, otherwise we can't compare the conjugate complex number of Z + 10 / z = Z + 10 / Z. we get that (Z-Z ') (1-10 / (Z * Z')) = 0, so when z = Z ', that is, B = 0, Z * Z' = 10, that is, a ^ 2 + B ^ 2 = 10, a = 1, B = 3 or a = 3, B = 1z = 1 + 3I or 3 + I satisfies the condition 1 ＜ (Z + 10 / z) ≤ 6 when B =