z=-5+3i 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=◻" 。 "

Question

z=-5+3i 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 = -5 + 3i, where the real part is -5 and the imaginary part is 3.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(3 / -5).Find theta in radians: Use a calculator to find the value of theta in radians. theta = arctan(3 / -5) ≈ arctan(-0.6).Convert angle to degrees: Convert the angle from radians to degrees. theta ≈ arctan(-0.6) * (180 / π) degrees.Ensure angle range: Calculate the angle in degrees and ensure it is within the specified range of -180° to 180°. Since the complex number is in the second quadrant (real part is negative, imaginary part is positive), we add 180° to the calculated angle to get the angle in the correct range. theta ≈ arctan(-0.6) * (180 / π) + 180 degrees.Find final theta in degrees: Use a calculator to find the final value of theta in degrees. theta ≈ arctan(-0.6) * (180 / π) + 180 ≈ -30.96 + 180 ≈ 149.04 degrees.

$z=-5+3 i$ $\newline$ 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 $-180^{\circ}$ and $180^{\circ}$ . $\newline$ $\theta=\square^{\circ}$

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