Find the argument of the complex number 2+2i in the interval 0

Question

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

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Understand Complex Number Argument: Understand the concept of the argument of a complex number. The argument of a complex number z = a + bi, where a and b are real numbers, is the angle θ in polar coordinates that the line connecting the origin to the point (a, b) makes with the positive real axis. The argument is usually denoted as arg(z) and is measured in radians.Convert to Polar Form: Convert the complex number to polar form to find the argument. For the complex number 2+2i, we can find the argument by calculating the angle θ using the formula θ = arctan(b/a), where a is the real part and b is the imaginary part of the complex number.Calculate Using Arctan: Calculate the argument using the arctan function. For the complex number 2+2i, a = 2 and b = 2. Therefore, θ = arctan(2/2) = arctan(1).Evaluate Arctan of 1: Evaluate the arctan of 1. The arctan of 1 is π/4 radians because the tangent of π/4 is 1. This is a well-known value from trigonometry.Ensure Correct Interval: Ensure the argument is in the correct interval. Since we are looking for the argument in the interval 0 <= θ < 2π, and π/4 is already in this interval, we do not need to adjust the value of the argument.Write Final Answer: Write the final answer. The argument of the complex number 2+2i is π/4 radians.

Find the argument of the complex number $2+2 i$ in the interval 0 \leq \theta<2 \pi . Express your answer in terms of $\pi$ .

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Find the argument of the complex number 2+2i 2+2 i 2+2i in the interval 0 \leq \theta<2 \pi . Express your answer in terms of π \pi π.

Find the argument of the complex number $2+2 i$ in the interval 0 \leq \theta<2 \pi . Express your answer in terms of $\pi$ .