Write a function to polar that accepts a complex number c, and returns two output arguments containing the magnitude mag and angle theta of the complex number. The output angle should be in degrees.

Short Answer

Expert verified
To create a function named 'to_polar' that accepts a complex number \(c\), and returns the magnitude (mag) and angle (theta) in degrees, follow these steps: 1. Define the function signature: \(to\_polar(c)\), where \(c\) is a complex number. 2. Extract the real and imaginary parts of \(c\): \(a = \text{Re}(c)\) and \(b = \text{Im}(c)\). 3. Calculate the magnitude using the formula: \(\text{mag} = \sqrt{a^2 + b^2}\). 4. Calculate the angle in radians: \(\text{theta} = \arctan\left(\frac{b}{a}\right)\). 5. Convert the angle to degrees: \(\text{theta (degrees)} = \text{theta (radians)} \cdot \frac{180}{\pi}\). 6. Return the magnitude and angle in degrees as output. The function can be implemented in Python as follows: ```python import cmath import math def to_polar(c): a = c.real b = c.imag mag = math.sqrt(a**2 + b**2) theta_radians = math.atan2(b, a) theta_degrees = math.degrees(theta_radians) return mag, theta_degrees ```

Step by step solution

01

Understand complex number in rectangular form

A complex number is represented as \(c = a + bi\), where \(a\) and \(b\) are real numbers, and \(i\) is the imaginary unit (\(i^2 = -1\)). A complex number in rectangular form can be represented as a point in the complex plane with coordinates \((a, b)\).
02

Understand complex number in polar form

A complex number can also be represented in polar form as \(c = \text{mag} \cdot e^{i\cdot \text{theta}}\), where \(\text{mag}\) is the magnitude of the complex number and \(\text{theta}\) is the angle between the real axis and the line connecting the origin and the point representing the complex number. The magnitude can be calculated using the Pythagorean theorem: \[\text{mag} = \sqrt{a^2 + b^2}\]To find the angle in radians, we can use the arctangent function: \[\text{theta} = \arctan\left(\frac{b}{a}\right)\]To convert the angle to degrees, use the following conversion: \[\text{theta (degrees)} = \text{theta (radians)} \cdot \frac{180}{\pi}\]
03

Create the function to_polar

To create the function, follow these steps: 1. Define the function signature: \(to\_polar(c)\), where \(c\) is a complex number. 2. Extract the real and imaginary parts of \(c\): \(a = \text{Re}(c)\) and \(b = \text{Im}(c)\). 3. Calculate the magnitude using the formula: \(\text{mag} = \sqrt{a^2 + b^2}\). 4. Calculate the angle in radians: \(\text{theta} = \arctan\left(\frac{b}{a}\right)\). 5. Convert the angle to degrees: \(\text{theta (degrees)} = \text{theta (radians)} \cdot \frac{180}{\pi}\). 6. Return the magnitude and angle in degrees as output. Function implementation: ```python import cmath import math def to_polar(c): a = c.real b = c.imag mag = math.sqrt(a**2 + b**2) theta_radians = math.atan2(b, a) theta_degrees = math.degrees(theta_radians) return mag, theta_degrees ``` Now you have the to_polar function that will take a complex number as input and return its magnitude and angle in degrees.

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Most popular questions from this chapter

In a sinusoidal steady-state AC circuit, the voltage across a passive element is given by Ohm's law: where \(\mathbf{V}\) is the voltage across the element, \(\mathbf{I}\) is the current through the element, and \(Z\) is the impedance of the clement. Note that all three of these values are complex, and that these complex numbers are usually specified in the form of a magnitude at a specific phase angle expressed in degrees. For example, the voltage might be \(\mathbf{V}=120 \angle 30^{\circ} \mathrm{V}\). Write a program that reads the voltage across an element and the impedance of the element, and calculates the resulting current flow. The input values should be given as magnitudes and angles expressed in degrees, and the resulting answer should be in the same form. Use the function to_complex from Exercise \(6.3\) to convert the numbers to rectangular for the actual computation of the current, and the function to polar from Exercise \(6.2\) to convert the answer into polar form for display (see Figure \(6.13\) ),

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Write a program that accepts a string from a user with the input function, chops that string into a series of tokens, sorts the tokens into ascending order, and prints them out.

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