z=-3-6i Find the angle theta (in radians) that z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express theta between -pi and pi. theta=

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z=-3-6i Find the angle  theta (in radians) that  z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express  theta between  -pi and  pi.  theta=

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Identify real and imaginary parts: To find the angle theta that the complex number z = -3 - 6i makes with the positive x-axis in the complex plane, we need to use the arctangent function, which gives us the angle in radians for a given ratio of the imaginary part to the real part of a complex number. The formula to find the angle is theta = atan2(imaginary part, real part).Use atan2 function: First, identify the real part and the imaginary part of the complex number z = -3 - 6i. The real part is -3 and the imaginary part is -6.Calculate theta: Now, use the atan2 function to find the angle. The atan2 function takes into account the signs of both the real and imaginary parts to determine the correct quadrant for the angle. theta = atan2(-6, -3)Determine the quadrant: Calculate the value of theta using the atan2 function. theta = atan2(-6, -3)Find the angle theta: The atan2 function will return a value in radians. Since the real part and the imaginary part are both negative, the angle theta will be in the third quadrant. The atan2 function will automatically give us an angle in the correct range between -pi and pi.After calculating, we find that the angle theta is approximately -2.034 radians. This is the angle that z makes with the positive x-axis in the complex plane, and it is expressed between -pi and pi.

$z=-3-6 i$ $\newline$ Find the angle $\theta$ (in radians) that $z$ makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express $\theta$ between $-\pi$ and $\pi$ . $\newline$ $\theta=$

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z=−3−6i z=-3-6 i z=−3−6i\newlineFind the angle θ \theta θ (in radians) that z z z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express θ \theta θ between −π -\pi −π and π \pi π.\newlineθ= \theta= θ=

$z=-3-6 i$ $\newline$ Find the angle $\theta$ (in radians) that $z$ makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express $\theta$ between $-\pi$ and $\pi$ . $\newline$ $\theta=$