z=-7-6i 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=-7-6i 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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Understand the problem: Understand the problem. We need to find the angle θ that the complex number z = -7 - 6i makes with the positive x-axis in the complex plane. This angle is also known as the argument of the complex number.Represent in complex plane: Represent the complex number in the complex plane. The complex number z = -7 - 6i can be represented as a point in the complex plane with coordinates (-7, -6). The angle θ we are looking for is the angle between the positive x-axis and the line segment from the origin to the point (-7, -6), measured in the counter-clockwise direction.Calculate using arctangent: Calculate the angle using the arctangent function. The angle θ can be found using the arctangent of the imaginary part divided by the real part of the complex number. However, since the complex number is in the third quadrant, we need to add 180° to the result of the arctangent to get the correct angle in the range of -180° to 180°. θ = atan2(-6, -7) + 180°Use calculator to find angle: Use a calculator to find the angle. Using a calculator with the atan2 function, we input the imaginary part (-6) and the real part (-7) to get the angle in radians. Then we convert it to degrees and add 180°. θ = atan2(-6, -7) * (180/π) + 180°Perform calculation and round: Perform the calculation and round if necessary. θ ≈ atan2(-6, -7) * (180/π) + 180° θ ≈ -139.4° + 180° θ ≈ 40.6° Since the angle needs to be between -180° and 180°, and our result is 40.6°, we do not need to adjust it further.

$z=-7-6 i$ $\newline$ 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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