The argument of a complex number is the angle between the positive real axis and the vector representing the complex number. In this case, the complex number is in the form a+bi, where a is the real part and bi is the imaginary part. To find the argument, we can use the formula tanθ = b/a, where θ is the argument and a and b are the real and imaginary parts, respectively. In this case, a=-4√3 and b=-4. Therefore, the argument is θ = tan^-1(-4/-4√3) = tan^-1(1/√3) = π/6 radians or 30 degrees.
Yes, the argument of a complex number can be negative. This is because the argument is measured counterclockwise from the positive real axis. If the complex number lies in the third or fourth quadrant, the argument will be negative.
To convert the argument from radians to degrees, we can use the formula θ (in degrees) = θ (in radians) * 180/π. In this case, the argument is π/6 radians, so θ (in degrees) = (π/6) * (180/π) = 30 degrees.
The argument of a complex number is significant in representing the direction or angle of the vector representing the complex number. It is also useful in finding the roots of a complex number or in solving equations involving complex numbers.
Yes, the argument of a complex number can be greater than 360 degrees. This is because the argument is measured counterclockwise from the positive real axis, so it can have multiple rotations around the origin. In this case, the argument is 30 degrees, which is equivalent to 1 rotation (360 degrees) plus 30 degrees.