z=5-3i 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=◻^(@)

Calculate Argument: To find the angle theta that the complex number z = 5 - 3i makes in the complex plane, we need to calculate the argument of the complex number, which is the angle formed with the positive x-axis (real axis).Use Arctan Function: The argument of a complex number z = a + bi is given by theta = arctan(b/a), where a is the real part and b is the imaginary part of the complex number. For z = 5 - 3i, a = 5 and b = -3.Check Angle Range: We calculate theta = arctan(-3/5). Using a calculator, we find that arctan(-3/5) ≈ -30.96 degrees. However, we need to ensure that the angle is expressed between -180 degrees and 180 degrees.Determine Quadrant: Since the complex number 5 - 3i is located in the fourth quadrant of the complex plane (because the real part is positive and the imaginary part is negative), the angle we found is already in the correct range. Therefore, we do not need to adjust the angle.Round to Nearest Tenth: We round the angle to the nearest tenth, which gives us theta ≈ -30.96 ≈ -31.0 degrees.

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z=5-3i
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=◻^(@)

$z=5-3i$ $\newline$ 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 $\newline$ $-180^\circ$ and $180^\circ$ . $\newline$ $\theta=\square^\circ$

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Math Problems

Algebra 2

Sin, cos, and tan of special angles

Full solution

z=5-3i

\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

\newline

-180^\circ

and

180^\circ

\newline

\theta=\square^\circ

Calculate Argument: To find the angle $\theta$ that the complex number $z = 5 - 3i$ makes in the complex plane, we need to calculate the argument of the complex number, which is the angle formed with the positive $x$ -axis (real axis).
Use Arctan Function: The argument of a complex number $z = a + bi$ is given by $\theta = \arctan(\frac{b}{a})$ , where $a$ is the real part and $b$ is the imaginary part of the complex number. For $z = 5 - 3i$ , $a = 5$ and $b = -3$ .
Check Angle Range: We calculate $\theta = \arctan(-\frac{3}{5})$ . Using a calculator, we find that $\arctan(-\frac{3}{5}) \approx -30.96$ degrees. However, we need to ensure that the angle is expressed between $-180$ degrees and $180$ degrees.
Determine Quadrant: Since the complex number $5 - 3i$ is located in the fourth quadrant of the complex plane (because the real part is positive and the imaginary part is negative), the angle we found is already in the correct range. Therefore, we do not need to adjust the angle.
Round to Nearest Tenth: We round the angle to the nearest tenth, which gives us $\theta \approx -30.96 \approx -31.0$ degrees.