z=4-2i 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=◻" 。 "

Question

z=4-2i 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 Complex Number: Identify the real and imaginary parts of the complex number z = 4 - 2i. The real part is 4, and the imaginary part is -2.Calculate Angle Using Arctangent: Calculate the angle theta using the arctangent function, which gives the angle in radians for a given tangent value. The tangent of the angle is the ratio of the imaginary part to the real part. theta = arctan(imaginary part / real part) = arctan(-2 / 4)Perform Arctangent Calculation: Perform the calculation for the arctangent. theta = arctan(-2 / 4) = arctan(-0.5) Use a calculator to find the value of theta in radians.Convert Angle to Degrees: Convert the angle from radians to degrees. Since 180 degrees is equivalent to pi radians, we can use the conversion factor 180/pi to convert our angle from radians to degrees. theta (in degrees) = theta (in radians) * (180/pi)Round Angle to Nearest Tenth: Round the angle to the nearest tenth, if necessary, and ensure it is expressed between -180° and 180°. If the calculated angle is not within this range, adjust it by adding or subtracting 360° until it falls within the desired range.

$z=4-2 i$ $\newline$ 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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