z=-2-5i Find the angle theta (in radians) that z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express theta between -pi and pi. theta=

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z=-2-5i Find the angle  theta (in radians) that  z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express  theta between  -pi and  pi.  theta=

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Calculate Argument of z: To find the angle theta, we need to calculate the argument of the complex number z=-2-5i. The argument is the angle the complex number makes with the positive x-axis in the complex plane.Determine Quadrant for Angle: The argument of a complex number a+bi is given by arctan(b/a), but since our a is negative and b is negative, the angle will be in the third quadrant. We need to add pi to the arctan value to get the correct angle in the range of -pi to pi.Calculate Arctan Value: First, calculate the arctan value: arctan(5/2). This is the angle in the first quadrant, but we need the angle in the third quadrant.Adjust Angle for Third Quadrant: Using a calculator, we find arctan(5/2) ≈ 1.190.Add Pi to Arctan Value: Since the angle is in the third quadrant, we add pi to get the angle in the correct range: 1.190 + pi.Calculate Final Angle: Adding 1.190 to pi gives us approximately 1.190 + 3.142 = 4.332.Ensure Angle Range: However, we need to ensure the angle is between -pi and pi. Since 4.332 is greater than pi, we subtract 2*pi to get the angle in the correct range.Final Angle Calculation: Subtracting 2*pi from 4.332 gives us 4.332 - 2*3.142 = -1.952.

$z=-2-5 i$ $\newline$ Find the angle $\theta$ (in radians) that $z$ makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express $\theta$ between $-\pi$ and $\pi$ . $\newline$ $\theta=$

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z=−2−5i z=-2-5 i z=−2−5i\newlineFind the angle θ \theta θ (in radians) that z z z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express θ \theta θ between −π -\pi −π and π \pi π.\newlineθ= \theta= θ=

$z=-2-5 i$ $\newline$ Find the angle $\theta$ (in radians) that $z$ makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express $\theta$ between $-\pi$ and $\pi$ . $\newline$ $\theta=$