z=3-4i 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=3-4i 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 Parts of z: Identify the real and imaginary parts of the complex number z. z = 3 - 4i, where the real part is 3 and the imaginary part is -4.Calculate Magnitude of z: Calculate the magnitude of z. The magnitude of z is given by the square root of the sum of the squares of the real and imaginary parts. |z| = sqrt(3^2 + (-4)^2) = sqrt(9 + 16) = sqrt(25) = 5.Find Theta Using Definition: Use the definition of the argument of a complex number to find theta. The argument of a complex number, theta, is the angle the line connecting the origin to the point (real, imaginary) makes with the positive real axis. theta = arctan(imaginary part / real part) = arctan(-4 / 3).Calculate Theta with Arctan: Calculate theta using the arctan function. theta = arctan(-4 / 3). Since the complex number is in the fourth quadrant (real part is positive, imaginary part is negative), we need to add pi to the result of arctan to get the angle in the correct range. theta = arctan(-4 / 3) + pi.Use Calculator for Theta: Use a calculator to find the value of theta. theta = arctan(-4 / 3) + pi ≈ -0.927 + 3.142 ≈ 2.215 (rounded to the nearest thousandth).Verify Theta Range: Verify that theta is within the correct range. The range for theta is between -pi and pi. Since 2.215 is within this range, our answer is valid.

$z=3-4 i$ $\newline$ 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=3−4i z=3-4 i z=3−4i\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=

$z=3-4 i$ $\newline$ 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 $\pi$ . $\newline$ $\theta=$