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Find the argument of the complex number -3sqrt3+0i in the interval 0 <= theta < 2pi. Express your answer in terms of pi. Answer:

Find the argument of the complex number −33+0i -3 \sqrt{3}+0 i in the interval 0≤θ<2π 0 \leq \theta<2 \pi . Express your answer in terms of π \pi .\newlineAnswer:

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Q. Find the argument of the complex number −33+0i -3 \sqrt{3}+0 i in the interval 0≤θ<2π 0 \leq \theta<2 \pi . Express your answer in terms of π \pi .\newlineAnswer:
  1. Definition of Argument: The argument of a complex number is the angle the line representing the number makes with the positive real axis in the complex plane. The complex number given is −33+0i-3\sqrt{3} + 0i, which lies on the negative real axis.
  2. Identification of Quadrant: Since the complex number is purely real and negative, the argument is not in the first quadrant 00 to π/2\pi/2) or the second quadrant π/2\pi/2 to π\pi), but it is on the line that divides the second and third quadrants, which corresponds to an angle of π\pi.
  3. Calculation of Argument: The argument of the complex number −33+0i-3\sqrt{3} + 0i is therefore π\pi radians, which is within the specified interval of 0≤θ<2π0 \leq \theta < 2\pi.

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