A question in the plural The equation x ^ 2 + ax + 4 + 3I = 0 of X has real roots, and the minimum of modulus of complex a is obtained

A question in the plural The equation x ^ 2 + ax + 4 + 3I = 0 of X has real roots, and the minimum of modulus of complex a is obtained

Let a = m + Ni
x'2+(m+ni)x+4+3i=0
x'2+mx+4=0
nx+3=0
M = - x-4 / X
n=-3/x
And a is module = radical (m'2 + n'2) = radical (x'2 + 25 / X'2 + 8)
x'2+25/x'2>=10
So the minimum value of the module of a is the root sign 18, that is, the root sign 2