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z=5+7i 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=

z=5+7i z=5+7 i \newlineFind the angle θ \theta (in radians) that z z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express θ \theta between −π -\pi and π \pi .\newlineθ= \theta=

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Q. z=5+7i z=5+7 i \newlineFind the angle θ \theta (in radians) that z z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express θ \theta between −π -\pi and π \pi .\newlineθ= \theta=
  1. Identify Parts of zz: Identify the real and imaginary parts of the complex number zz.z=5+7iz = 5 + 7i, where the real part is 55 and the imaginary part is 77.
  2. Calculate Angle Theta: Calculate the angle theta using the arctangent function.\newlineThe angle theta in the complex plane is given by the arctangent of the imaginary part divided by the real part, which is arctan⁡(75)\arctan(\frac{7}{5}).
  3. Use Arctangent Function: Use a calculator to find the value of arctan⁡(75)\arctan(\frac{7}{5}).θ=arctan⁡(75)≈0.9505\theta = \arctan(\frac{7}{5}) \approx 0.9505 radians. Since the complex number is in the first quadrant (both real and imaginary parts are positive), the angle is positive and there is no need to adjust the range.

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