The argument of the complex number z = -1 - i is?

The argument of the complex number z = -1 - i is?

Step 1: Identify the complex number z, which is given as z = -1 - i.
Step 2: Recognize that the complex number can be represented in the form z = x + yi, where x = -1 and y = -1.
Step 3: Determine the coordinates of the complex number in the complex plane: (-1, -1).
Step 4: Find the angle θ (argument) using the formula θ = tan^(-1)(y/x). Here, y = -1 and x = -1.
Step 5: Substitute the values into the formula: θ = tan^(-1)(-1/-1) = tan^(-1)(1).
Step 6: The angle for tan^(-1)(1) is π/4, but since both x and y are negative, the angle is in the third quadrant.
Step 7: Adjust the angle for the third quadrant: θ = π + π/4 = 5π/4.
Step 8: Alternatively, you can express the angle as a negative angle: θ = -3π/4, which is equivalent.

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