z=-8+3i 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=-8+3i 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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Identify parts of z: Identify the real and imaginary parts of the complex number z. z = -8 + 3i, where the real part is -8 and the imaginary part is 3.Calculate angle theta: Calculate the angle theta using the arctangent function. The angle theta in the complex plane is given by the arctangent of the imaginary part divided by the real part, which is arctan(3/-8). However, since the real part is negative and the imaginary part is positive, the angle lies in the second quadrant.Use arctangent function: Use a calculator to find the arctangent of 3/-8. theta = arctan(3/-8) ≈ arctan(-0.375)Calculate theta in radians: Calculate the approximate value of theta in radians. theta ≈ -0.359 (in radians, using a calculator)Adjust angle in quadrant: Adjust the angle to lie in the correct quadrant. Since the angle is in the second quadrant, we need to add pi to the calculated value to get the angle between -pi and pi. theta = -0.359 + piCalculate final theta: Calculate the final value of theta. theta ≈ -0.359 + 3.142 (using the approximation pi ≈ 3.142) theta ≈ 2.783 (in radians)

$z=-8+3 i$ $\newline$ 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=−8+3i z=-8+3 i z=−8+3i\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=

$z=-8+3 i$ $\newline$ 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 $\pi$ . $\newline$ $\theta=$