Answer :
For this case we have that by definition, the discriminant of a quadratic expression is given by:
[tex]d = b ^ 2-4 (a) (c)[/tex]
If the discriminant is less than zero then the expression has two different complex roots.
In this case we have the following expression:
[tex]x ^ 2 + 4x + c[/tex]
So we have to:
[tex]a = 1\\b = 4\\c = c\\[/tex]
The discriminant is given by:
[tex]d = 4 ^ 2-4 (1) (c)\\d = 16-4c[/tex]
Then, if we want two complex roots it must be fulfilled that:
[tex]16-4c <0\\16 <4c\\\frac {16} {4} <c\\4 <c[/tex]
Thus, the expression has two complex roots for all values greater than 4.
ANswer:
[tex]c> 4[/tex]