z=-8+5i 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=-8+5i 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 parts of z: Identify the real and imaginary parts of the complex number z. z = -8 + 5i, where the real part is -8 and the imaginary part is 5.Calculate 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(5 / -8).Find theta in radians: Use a calculator to find the value of theta in radians. theta = arctan(5 / -8) ≈ arctan(-0.625).Convert angle to degrees: Convert the angle from radians to degrees. theta ≈ arctan(-0.625) * (180 / π) degrees.Calculate angle in degrees: Calculate the angle in degrees, ensuring it is in the correct quadrant. Since the real part is negative and the imaginary part is positive, z lies in the second quadrant. The arctan function will give a negative result because the tangent is negative in the second quadrant. To find the angle in the second quadrant, we add 180 degrees to the result. theta ≈ arctan(-0.625) * (180 / π) + 180 degrees.Perform calculation: Perform the calculation using a calculator. theta ≈ arctan(-0.625) * (180 / π) + 180 ≈ -32.0053832 + 180 ≈ 147.9946168 degrees.Round to nearest tenth: Round the answer to the nearest tenth. theta ≈ 148.0 degrees.

$z=-8+5 i$ $\newline$ 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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