Write a function that will accept a complex number \(c\) and plot that point oa a Cartesian coordinate system with a circular marker. The plot should include both the \(x\) and \(y\) axes, plus a vector drawn from the origin to the location of \(\mathrm{c}\).

A complex number is of the form \(c = a + bi\), where \(a\) is the real part and \(b\) is the imaginary part. You can split \(c\) into these two parts by simply identifying the values of \(a\) and \(b\).

Using the real part, \(a\), as the x-coordinate, and the imaginary part, \(b\), as the y-coordinate, you can plot the complex number on a 2D plane. Now that we know how to convert the complex number into Cartesian coordinates, we can write a function in Python using a plotting library like Matplotlib to draw the axes, the point, and the vector. ```python import numpy as np import matplotlib.pyplot as plt def plot_complex_number(c: complex): # Step 1: Find the real and imaginary parts of the complex number a, b = c.real, c.imag # Step 2: Plot the point on a Cartesian coordinate system fig, ax = plt.subplots() ax.set_aspect("equal") ax.axhline(0, color='black', linewidth=1) ax.axvline(0, color='black', linewidth=1) ax.set_xlim(-10, 10) ax.set_ylim(-10, 10) # Plot circular marker at the complex number's location ax.plot(a, b, 'bo', markersize=8) # Plot vector from the origin to the complex number's location ax.quiver(0, 0, a, b, angles='xy', scale_units='xy', scale=1, color='r') plt.xlabel('Real') plt.ylabel('Imaginary') plt.title(f'Complex number: {c}') plt.grid(True) plt.show() # Example usage plot_complex_number(3 + 4j) ``` This Python function takes a complex number as input and follows the steps mentioned earlier to plot the point on a Cartesian coordinate system, including a vector from the origin to the point. The output is a visual representation of the input complex number.