Final answer:
The argument of the complex number z = 4 + 4√3i is π/3 radians or 60 degrees, which is found using the arctangent of the ratio of the imaginary part to the real part.
Step-by-step explanation:
The value of the argument of a complex number z is the angle θ between the positive real axis and the line representing the complex number in the complex plane. For the complex number z = 4 + 4√3i, the argument θ can be found using the arctangent function, tan-1(y/x), where y is the imaginary part and x is the real part of the complex number.
In this case, the imaginary part is 4√3 and the real part is 4, giving us an argument θ = tan-1(4√3 / 4) which simplifies to tan-1(√3). This is a well-known angle, which is 60 degrees or π/3 radians. Therefore, the argument of the complex number z = 4 + 4√3i is π/3 radians or 60 degrees.