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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=◻" 。 "

$z=4-2 i$ $\newline$ 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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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q.

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}

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. $\newline$ The tangent of the angle is the ratio of the imaginary part to the real part. $\newline$ $\theta = \text{arctan}(\frac{\text{imaginary part}}{\text{real part}}) = \text{arctan}(\frac{-2}{4})$
Perform Arctangent Calculation: Perform the calculation for the arctangent. $\newline$ $\theta = \arctan(-2 / 4) = \arctan(-0.5)$ $\newline$ 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 $ext{pi}$ radians, we can use the conversion factor rac{180}{ ext{pi}} to convert our angle from radians to degrees. $\theta$ (in degrees) = $\theta$ (in radians) * (rac{180}{ ext{pi}})
Round Angle to Nearest Tenth: Round the angle to the nearest tenth, if necessary, and ensure it is expressed between $-180^\circ$ and $180^\circ$ . If the calculated angle is not within this range, adjust it by adding or subtracting $360^\circ$ until it falls within the desired range.

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