Find the argument of the complex number 3sqrt2+3sqrt2i in the interval 0

Question

Find the argument of the complex number  3sqrt2+3sqrt2i in the interval  0 <= theta < 2pi. Express your answer in terms of  pi. Answer:

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Given Complex Number: We are given a complex number in the form a + bi, where a = 3sqrt2 and b = 3sqrt2. The argument of a complex number is the angle θ in polar coordinates that the vector representing the complex number makes with the positive real axis. The argument can be found using the arctan function, which gives the angle in radians.Determine Quadrant: Since both the real and imaginary parts of the complex number are positive and equal, the complex number lies on the line y = x in the first quadrant of the complex plane. This means that the argument θ is 45 degrees or π/4 radians. However, we need to ensure that this is the correct angle for the given interval 0 <= theta < 2pi.Convert Degrees to Radians: To convert 45 degrees to radians, we use the fact that π radians is equal to 180 degrees. Therefore, 45 degrees is (45/180) * π = π/4 radians. Since this angle is in the first quadrant and within the specified interval, it is the correct argument for the complex number.Confirm Correctness: We can confirm that there is no math error by checking that the real and imaginary parts are equal and positive, which places the complex number in the first quadrant, and that the angle we found is indeed in the interval 0 <= theta < 2pi.

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

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