z=-3-8i Find the angle theta (in degrees) that z makes in the complex plane. Round your answer, if necessary, to the nearest tenth. Express theta between -180^(@) and 180^(@). theta=◻" 。 "

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z=-3-8i Find the angle  theta (in degrees) that  z makes in the complex plane. Round your answer, if necessary, to the nearest tenth. Express  theta between  -180^(@) and  180^(@).  theta=◻" 。 "

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Identify real and imaginary parts: Identify the real and imaginary parts of the complex number z. z = -3 - 8i, where the real part is -3 and the imaginary part is -8.Calculate the argument of z: Calculate the argument of z, which is the angle theta in the complex plane. The argument of z is given by theta = arctan(imaginary part / real part) = arctan(-8 / -3).Use calculator to find theta in radians: Use a calculator to find the value of theta in radians. theta = arctan(-8 / -3) = arctan(8 / 3). Since we need the angle in degrees, we will convert it after calculation.Convert radians to degrees: Convert the angle from radians to degrees. theta in degrees = arctan(8 / 3) * (180 / π).Calculate theta in degrees: Calculate the angle theta in degrees using a calculator. theta in degrees ≈ arctan(8 / 3) * (180 / π) ≈ 69.4°. However, since both the real and imaginary parts of z are negative, z lies in the third quadrant, and the angle should be adjusted to be between -180° and 180°.Adjust angle for correct quadrant: Adjust the angle for the correct quadrant. In the third quadrant, the angle theta should be negative and we add 180° to the calculated angle to get the angle in the correct range. theta = 69.4° - 180° = -110.6°.

$z=-3-8 i$ $\newline$ Find the angle $\theta$ (in degrees) that $z$ makes in the complex plane. $\newline$ Round your answer, if necessary, to the nearest tenth. Express $\theta$ between $-180^{\circ}$ and $180^{\circ}$ . $\newline$ $\theta=\square^{\circ}$

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