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=◻" 。 "

Question

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=◻" 。 "

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Understand the problem: Understand the problem. We need to find the angle theta that the complex number z = 5 - 3i makes with the positive x-axis in the complex plane. This angle is also known as the argument of the complex number.Convert to polar form: Convert the complex number to polar form. To find the angle theta, we can convert the complex number from rectangular form (a + bi) to polar form (r(cos(theta) + i*sin(theta))). The angle theta is the arctan of the imaginary part divided by the real part.Calculate angle with arctan: Calculate the angle using the arctan function. theta = arctan(-3/5) We use the arctan function because it gives us the angle whose tangent is the quotient of the imaginary part and the real part of the complex number.Use calculator for angle: Use a calculator to find the angle. theta = arctan(-3/5) ≈ arctan(-0.6) Using a calculator, we find that theta ≈ -30.96 degrees.Adjust angle within range: Adjust the angle to be within the specified range. Since the angle must be between -180° and 180°, and our calculated angle is already within this range, no further adjustment is necessary.Round angle if necessary: Round the angle to the nearest tenth, if necessary. theta ≈ -30.96 degrees ≈ -31.0 degrees when rounded to the nearest tenth.

$z=5-3 i$ $\newline$ 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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