The argument of a complex number is the angle between the positive real axis and the vector representing the number in the complex plane. In this case, the argument of sin(8π/5) + i is 8π/5 radians or 288 degrees in the fourth quadrant.
To solve the argument of a complex number, you can use the inverse tangent function (arctan). First, find the ratio of the imaginary and real parts of the complex number (i.e. sin(8π/5) = 1/2 and cos(8π/5) = -√3/2). Then, use the inverse tangent function to find the angle in radians or degrees.
Yes, the argument of a complex number can be negative. This indicates that the vector representing the complex number is in either the second or third quadrant of the complex plane.
The unit of measurement for the argument of a complex number is radians or degrees. Radians are the most commonly used unit for arguments, but degrees can also be used.
The argument of a complex number and its magnitude (or absolute value) are independent of each other. The argument represents the angle in the complex plane, while the magnitude represents the distance from the origin. However, both the argument and magnitude are necessary to fully describe a complex number.