z=1-2i 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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z=1-2i 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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Calculate Argument: To find the angle theta that the complex number z = 1 - 2i makes in the complex plane, we need to calculate the argument of the complex number. The argument is the angle formed by the real axis and the line segment representing the complex number in the complex plane. We can use the arctangent function to find this angle, which is given by theta = atan2(imaginary part, real part).Identify Real and Imaginary Parts: First, identify the real part (x) and the imaginary part (y) of the complex number z = 1 - 2i. Here, the real part x is 1, and the imaginary part y is -2.Use Arctangent Function: Now, use the arctangent function with the two parts. The function atan2(y, x) takes into account the signs of both x and y to determine the correct quadrant for the angle. Calculate theta = atan2(-2, 1).Convert Radians to Degrees: Perform the calculation using a calculator or a software tool that can compute atan2. The result will be in radians, so we need to convert it to degrees by multiplying by 180/pi.Final Result: After performing the calculation, we find that theta ≈ atan2(-2, 1) * (180/pi) ≈ -63.4 degrees. This is the angle that z makes in the complex plane, and it is already expressed between -180 degrees and 180 degrees.

$z=1-2 i$ $\newline$ 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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