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

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 -3sqrt(3) + 0i, which lies on the negative real axis.Identification of Quadrant: Since the complex number is purely real and negative, the argument is not in the first quadrant (0 to pi/2) or the second quadrant (pi/2 to pi), but it is on the line that divides the second and third quadrants, which corresponds to an angle of pi.Calculation of Argument: The argument of the complex number -3sqrt(3) + 0i is therefore pi radians, which is within the specified interval of 0 <= theta < 2pi.

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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 $-3 \sqrt{3}+0 i$ in the interval 0 \leq \theta<2 \pi . Express your answer in terms of $\pi$ . $\newline$ Answer:

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Q. Find the argument of the complex number

-3 \sqrt{3}+0 i

in the interval

0 \leq \theta<2 \pi

. Express your answer in terms of

\pi

\newline

Answer:

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 $-3\sqrt{3} + 0i$ , which lies on the negative real axis.
Identification of Quadrant: Since the complex number is purely real and negative, the argument is not in the first quadrant $0$ to $\pi/2$ ) or the second quadrant $\pi/2$ to $\pi$ ), but it is on the line that divides the second and third quadrants, which corresponds to an angle of $\pi$ .
Calculation of Argument: The argument of the complex number $-3\sqrt{3} + 0i$ is therefore $\pi$ radians, which is within the specified interval of 0 \leq \theta < 2\pi.