z=-6-5i 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=-6-5i 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 = -6 - 5i has a real part of -6 and an imaginary part of -5.Calculate Angle using Arctangent: 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(imaginary/real). theta = arctan(-5/-6)Use Calculator for Theta: Use a calculator to find the value of theta. theta = arctan(-5/-6) = arctan(5/6) Since we are using a calculator, we need to ensure it is set to degree mode.Calculate Angle in Degrees: Calculate the angle in degrees. theta ≈ arctan(5/6) ≈ 39.8° However, since the complex number is in the third quadrant (both real and imaginary parts are negative), we need to add 180° to get the angle in the correct quadrant. theta = 39.8° + 180°Final Value of Theta: Calculate the final value of theta. theta = 39.8° + 180° = 219.8° Since we want the angle between -180° and 180°, we subtract 360° to get the angle in the desired range. theta = 219.8° - 360°Find Angle in Range: Find the final angle theta in the specified range. theta = -140.2° This is the angle that z makes in the complex plane, expressed between -180° and 180°.

$z=-6-5 i$ $\newline$ 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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