Final answer:
The argument of the complex number 0−4i is 270° or 3π/2 radians since it lies directly on the negative imaginary axis.
Step-by-step explanation:
The argument of a complex number in polar form corresponds to the angle θ made with the positive real axis. Given the complex number 0−4i, it lies on the negative imaginary axis. Conventionally, the argument of a point lying directly below the origin is 270° or π/2 radians.
To find this argument, you can use the arctangent function or recognize immediately that a point on the negative imaginary axis has an angle of 270° without it. Remember, the arctan function can also be written as tan−1, and in this case, the angle θ = tan−1(Im/Re), where Im is the imaginary part and Re is the real part of the complex number.
Since the real part is 0 and the imaginary part is −4, tan−1(−4/0) is undefined. Thus, we refer to the standard position of angles in the Cartesian plane and deduce that the angle is 270° or 3π/2 radians.